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    <title>Pinboard (Vaguery)</title>
    <link>https://pinboard.in/u:Vaguery/public/</link>
    <description>recent bookmarks from Vaguery</description>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2310.12687"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2206.10003"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2107.06188"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2102.06046"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2103.01235"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/1708.01559"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1305.5752"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1904.07242"/>
	<rdf:li rdf:resource="https://golem.ph.utexas.edu/category/2018/01/more_secrets_of_the_associahed.html"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1704.00640"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1701.09175"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1611.05971"/>
	<rdf:li rdf:resource="http://www.cgl.uwaterloo.ca/csk/projects/"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1507.02762"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1506.08518"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1411.3647"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1507.08374"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1504.06823"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1502.03792"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1501.01891"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1404.0948"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1407.0224"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1403.6637"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1207.6452"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1007.2460"/>
	<rdf:li rdf:resource="http://www.zwoje-scrolls.com/zwoje44/text23.htm"/>
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  </channel><item rdf:about="https://arxiv.org/abs/2110.01069">
    <title>[2110.01069] Hinged Truchet tiling fractals</title>
    <dc:date>2024-08-08T13:34:42+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.01069</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This article describes a new method of producing space filling fractal dragon curves based on a hinged tiling procedure. The fractals produced can be generated by a simple L-system. The construction as a hinged tiling has the advantage of automatically implying that the fractiles produced tessellate, and that the Heighway fractal dragon curve, and the other curves constructed by this method, do not cross themselves. This also gives a new limiting procedure to apply to certain Truchet tilings. I include the computation of the fractal dimension of the boundary of one of the curves, and describe an algorithm for computing the sim value of the fractal boundary of these curves. The curves produced are well known. The hinged tiling approach is new, as is the algorithm for computing the sim value.
]]></description>
<dc:subject>tiling fractals rather-interesting mathematical-recreations algorithms symmetry to-simulate to-write-about consider:planning consider:classification rewriting-systems nonlinear-dynamics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c4fb85354d7b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:fractals"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:planning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nonlinear-dynamics"/>
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<item rdf:about="https://arxiv.org/abs/2310.12687">
    <title>[2310.12687] Combinatorics of the Permutahedra, Associahedra, and Friends</title>
    <dc:date>2024-07-02T10:56:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2310.12687</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[I present an overview of the research I have conducted for the past ten years in algebraic, bijective, enumerative, and geometric combinatorics. The two main objects I have studied are the permutahedron and the associahedron as well as the two partial orders they are related to: the weak order on permutations and the Tamari lattice. This document contains a general introduction (Chapters 1 and 2) on those objects which requires very little previous knowledge and should be accessible to non-specialist such as master students. Chapters 3 to 8 present the research I have conducted and its general context. You will find:
* a presentation of the current knowledge on Tamari interval and a precise description of the family of Tamari interval-posets which I have introduced along with the rise-contact involution to prove the symmetry of the rises and the contacts in Tamari intervals;
* my most recent results concerning q, t-enumeration of Catalan objects and Tamari intervals in relation with triangular partitions;
* the descriptions of the integer poset lattice and integer poset Hopf algebra and their relations to well known structures in algebraic combinatorics;
* the construction of the permutree lattice, the permutree Hopf algebra and permutreehedron;
* the construction of the s-weak order and s-permutahedron along with the s-Tamari lattice and s-associahedron.
Chapter 9 is dedicated to the experimental method in combinatorics research especially related to the SageMath software. Chapter 10 describes the outreach efforts I have participated in and some of my approach towards mathematical knowledge and inclusion.
]]></description>
<dc:subject>combinatorics group-theory symmetry enumeration rather-interesting trees to-write-about consider:mutation-operators consider:rewriting-systems consider:coverage</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:8b207808104e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:trees"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:mutation-operators"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:coverage"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2206.10003">
    <title>[2206.10003] Folding rotationally symmetrical tableaux via webs</title>
    <dc:date>2022-09-28T10:20:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2206.10003</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Rectangular standard Young tableaux with 2 or 3 rows are in bijection with Uq(𝔰𝔩2)-webs and Uq(𝔰𝔩3)-webs respectively. When W is a web with a reflection symmetry, the corresponding tableau TW has a rotational symmetry. Folding TW transforms it into a domino tableau DW. We study the relationships between these correspondences. For 2-row tableaux, folding a rotationally symmetric tableau corresponds to "literally folding" the web along its axis of symmetry. For 3-row tableaux, we give simple algorithms, which provide direct bijective maps between symmetrical webs and domino tableaux (in both directions). These details of these algorithms reflect the intuitive idea that DW corresponds to "W modulo symmetry".
]]></description>
<dc:subject>combinatorics domino-tiling enumeration symmetry representation to-understand to-simulate consider:moves-as-text-transformations</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:41aba0acbdfd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:domino-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:moves-as-text-transformations"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2107.06188">
    <title>[2107.06188] The degree of asymmetry of sequences</title>
    <dc:date>2021-12-19T12:36:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.06188</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion for compositions, words, matchings, binary trees and permutations, we find generating functions enumerating these objects with respect to their degree of asymmetry, and we describe the limiting distribution of this statistic in each case.
]]></description>
<dc:subject>symmetry combinatorics rather-interesting feature-construction group-theory strings to-understand to-write-about consider:code</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:497a7b1767d6/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:code"/>
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<item rdf:about="https://theinnerframe.org/2020/08/26/alan-schoens-small-octons-solitaire-xxii-from-the-pillowbook-xvii/">
    <title>Alan Schoen’s Small Octons (Solitaire XXII – From the Pillowbook XVII) – The Inner Frame</title>
    <dc:date>2021-07-24T11:32:53+00:00</dc:date>
    <link>https://theinnerframe.org/2020/08/26/alan-schoens-small-octons-solitaire-xxii-from-the-pillowbook-xvii/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Above you can see how Alan decomposes a regular octahedron into octons. The recipe is the same as for the cubons and tetrons: Divide the edges of the octahedron in suitable ratios, connect the subdivision points to the face centers and the center of the octahedron. If you allow as subdivisions the proportions (1:2) and (2:1), there are six different octons that you can get this way.]]></description>
<dc:subject>puzzles solid-geometry mathematical-recreations models rather-interesting to-make symmetry combinatorics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:96ba9752e7bd/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:puzzles"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:solid-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-make"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2102.06046">
    <title>[2102.06046] A Quasiperiodic Tiling With 12-Fold Rotational Symmetry and Inflation Factor 1 + Sqrt(3)</title>
    <dc:date>2021-07-04T11:48:27+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.06046</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We show how we found substitution rules for a quasiperiodic tiling with local rotational symmetry and inflation factor 1 + sqrt(3). The base tiles are a square, a rhomb with an acute angle of 30 degrees, and equilateral triangles that are cut in half. These half-triangles follow three different substitution rules and can be recombined into equilateral triangles in nine different ways to make minor variations of the tiling. The tiling contains quasiperiodically repeated 12-fold rosettes. A central rosette can be enlarged to make an arbitrarily large tiling with 12-fold rotational symmetry. An online computer program is provided that allows the user to explore the tiling.
]]></description>
<dc:subject>aperiodic-tiling rewriting-systems rather-interesting symmetry to-write-about to-automate consider:performance-measures consider:arbitrary-starts consider:1-2-3-4-quads</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:634a72121f6d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aperiodic-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-automate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:arbitrary-starts"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:1-2-3-4-quads"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2103.01235">
    <title>[2103.01235] Statistical mechanics of dimers on quasiperiodic tilings</title>
    <dc:date>2021-07-04T11:08:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2103.01235</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study classical dimers on two-dimensional quasiperiodic Ammann-Beenker (AB) tilings. Despite the lack of periodicity we prove that each infinite tiling admits 'perfect matchings' in which every vertex is touched by one dimer. We introduce an auxiliary 'AB∗' tiling obtained from the AB tiling by deleting all 8-fold coordinated vertices. The AB∗ tiling is again two-dimensional, infinite, and quasiperiodic. The AB∗ tiling has a single connected component, which admits perfect matchings. We find that in all perfect matchings, dimers on the AB∗ tiling lie along disjoint one-dimensional loops and ladders, separated by 'membranes', sets of edges where dimers are absent. As a result, the dimer partition function of the AB∗ tiling factorizes into the product of dimer partition functions along these structures. We compute the partition function and free energy per edge on the AB∗ tiling using an analytic transfer matrix approach. Returning to the AB tiling, we find that membranes in the AB∗ tiling become 'pseudomembranes', sets of edges which collectively host at most one dimer. This leads to a remarkable discrete scale-invariance in the matching problem. The structure suggests that the AB tiling should exhibit highly inhomogenous and slowly decaying connected dimer correlations. Using Monte Carlo simulations, we find evidence supporting this supposition in the form of connected dimer correlations consistent with power law behaviour. Within the set of perfect matchings we find quasiperiodic analogues to the staggered and columnar phases observed in periodic systems.]]></description>
<dc:subject>domino-tiling tiling dynamical-systems rather-interesting quasicrystals aperiodic-tiling to-write-about consider:animation symmetry constraint-satisfaction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c0988dd4a678/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:domino-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:dynamical-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:quasicrystals"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aperiodic-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:animation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:constraint-satisfaction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2104.14863">
    <title>[2104.14863] Reconstruction of hypergraphs from line graphs and degree sequences</title>
    <dc:date>2021-05-07T16:20:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2104.14863</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper we consider the problem to reconstruct a k-uniform hypergraph from its line graph. In general this problem is hard. We solve this problem when the number of hyperedges containing any pair of vertices is bounded. Given an integer sequence, constructing a k-uniform hypergraph with that as its degree sequence is NP-complete. Here we show that for constant integer sequences the question can be answered in polynomial time using Baranyai's theorem.
]]></description>
<dc:subject>hypergraphs inference symmetry graph-theory rather-interesting inference? to-understand to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:9e7017d2e481/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:hypergraphs"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:inference?"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1811.00679">
    <title>[1811.00679] Arithmeticity and Hidden Symmetries of Fully Augmented Pretzel Link Complements</title>
    <dc:date>2020-10-03T12:09:20+00:00</dc:date>
    <link>https://arxiv.org/abs/1811.00679</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[This paper examines number theoretic and topological properties of fully augmented pretzel link complements. In particular, we determine exactly when these link complements are arithmetic and exactly which are commensurable with one another. We show these link complements realize infinitely many CM-fields as invariant trace fields, which we explicitly compute. Further, we construct two infinite families of non-arithmetic fully augmented link complements: one that has no hidden symmetries and the other where the number of hidden symmetries grows linearly with volume. This second family realizes the maximal growth rate for the number of hidden symmetries relative to volume for non-arithmetic hyperbolic 3-manifolds. Our work requires a careful analysis of the geometry of these link complements, including their cusp shapes and totally geodesic surfaces inside of these manifolds.
]]></description>
<dc:subject>topology knot-theory combinatorics to-understand purdy-pitchers symmetry no-really-I-can't-make-head-nor-tails-of-it</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:c5ab86a74aa6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:knot-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:purdy-pitchers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:no-really-I-can't-make-head-nor-tails-of-it"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1505.02029">
    <title>[1505.02029] Vertex-transitive graphs and their arc-types</title>
    <dc:date>2020-06-14T11:29:42+00:00</dc:date>
    <link>https://arxiv.org/abs/1505.02029</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Let X be a finite vertex-transitive graph of valency d, and let A be the full automorphism group of X. Then the arc-type of X is defined in terms of the sizes of the orbits of the action of the stabiliser Av of a given vertex v on the set of arcs incident with v. Specifically, the arc-type is the partition of d as the sum
n1+n2+⋯+nt+(m1+m1)+(m2+m2)+⋯+(ms+ms),
where n1,n2,…,nt are the sizes of the self-paired orbits, and m1,m1,m2,m2,…,ms,ms are the sizes of the non-self-paired orbits, in descending order. 
In this paper, we find the arc-types of several families of graphs. Also we show that the arc-type of a Cartesian product of two `relatively prime' graphs is the natural sum of their arc-types. Then using these observations, we show that with the exception of 1+1 and (1+1), every partition as defined above is realisable, in the sense that there exists at least one graph with the given partition as its arc-type.
]]></description>
<dc:subject>combinatorics symmetry algebra rather-interesting to-understand consider:visualization consider:hypergraphs</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:1a3e0e9b8b96/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:hypergraphs"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1708.01559">
    <title>[1708.01559] Spherical Geometry and the Least Symmetric Triangle</title>
    <dc:date>2019-09-09T10:43:14+00:00</dc:date>
    <link>https://arxiv.org/abs/1708.01559</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study the problem of determining the least symmetric triangle, which arises both from pure geometry and from the study of molecular chirality in chemistry. Using the correspondence between planar n-gons and points in the Grassmannian of 2-planes in real n-space introduced by Hausmann and Knutson, this corresponds to finding the point in the fundamental domain of the hyperoctahedral group action on the Grassmannian which is furthest from the boundary, which we compute exactly. We also determine the least symmetric obtuse and acute triangles. These calculations provide prototypes for computations on polygon and shape spaces.
]]></description>
<dc:subject>symmetry optimization rather-interesting define-your-terms performance-measure to-write-about to-emulate to-simulate consider:looking-to-see consider:robustness consider:stamp-collecting geometry plane-geometry</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:57d2fd877722/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:define-your-terms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:performance-measure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-emulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:robustness"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:stamp-collecting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:plane-geometry"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1305.5752">
    <title>[1305.5752] Symmetry detection of auxetic behaviour in 2D frameworks</title>
    <dc:date>2019-07-14T12:48:59+00:00</dc:date>
    <link>https://arxiv.org/abs/1305.5752</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry has Poisson's ratio -1, with equal expansion/contraction in all directions, and is here termed equiauxetic. A framework may have a symmetry-detectable equiauxetic mechanism if it belongs to a plane group that includes rotational axes of order n = 6, 4, or 3. If the reducible representation for the net mobility contains mechanisms that preserve full rotational symmetry (A modes), these are equiauxetic. In addition, for n = 6, mechanisms that halve rotational symmetry (B modes) are also equiauxetic.
]]></description>
<dc:subject>materials-science kinematics statics graph-theory rather-interesting feature-construction symmetry physics! simulation to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:74444fb0cc10/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:kinematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:statics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-construction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:physics!"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1904.07242">
    <title>[1904.07242] Topological phases without crystalline counterparts</title>
    <dc:date>2019-06-24T11:11:02+00:00</dc:date>
    <link>https://arxiv.org/abs/1904.07242</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Recent years saw the complete classification of topological band structures, revealing an abundance of topological crystalline insulators. Here we theoretically demonstrate the existence of topological materials beyond this framework, protected by quasicrystalline symmetries. We construct a higher-order topological phase protected by a point group symmetry that is impossible in any crystalline system. Our tight-binding model describes a superconductor on a quasicrystalline Ammann-Beenker tiling which hosts localized Majorana zero modes at the corners of an octagonal sample. The Majorana modes are protected by particle-hole symmetry and by the combination of an 8-fold rotation and in-plane reflection symmetry. We find a bulk topological invariant associated with the presence of these zero modes, and show that they are robust against large symmetry preserving deformations, as long as the bulk remains gapped. The nontrivial bulk topology of this phase falls outside all currently known classification schemes.]]></description>
<dc:subject>materials-science simulation classification ontology rather-interesting tiling symmetry out-of-the-box define-your-terms topology to-understand</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:4ad654213c8f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:materials-science"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:simulation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:ontology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:out-of-the-box"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:define-your-terms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:topology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://golem.ph.utexas.edu/category/2018/01/more_secrets_of_the_associahed.html">
    <title>More Secrets of the Associahedra | The n-Category Café</title>
    <dc:date>2018-02-02T13:43:52+00:00</dc:date>
    <link>https://golem.ph.utexas.edu/category/2018/01/more_secrets_of_the_associahed.html</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The associahedra are wonderful things discovered by Jim Stasheff around 1963 but even earlier by Dov Tamari in his thesis. They hold the keys to understanding ‘associativity up to coherent homotopy’ in exquisite combinatorial detail.

But do they still hold more secrets? I think so!

]]></description>
<dc:subject>group-theory mathematical-recreations open-questions symmetry to-write-about to-understand consider:visual-algorithms</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:b65b20dceff1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:open-questions"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:visual-algorithms"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1704.00640">
    <title>[1704.00640] Symmetric motifs in random geometric graphs</title>
    <dc:date>2017-12-03T13:50:54+00:00</dc:date>
    <link>https://arxiv.org/abs/1704.00640</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency spectrum as sharp, distinct peaks, a feature often found in real-world networks. We look at the probabilities of their appearance and compare these across parameter space and dimension. We then use the Chen-Stein method to derive the minimum separation distance in random geometric graphs which we apply to study symmetric motifs in both the intensive and thermodynamic limits. In the thermodynamic limit the probability that the closest nodes are symmetric approaches one, whilst in the intensive limit this probability depends upon the dimension.
]]></description>
<dc:subject>graph-theory network-theory rather-interesting probability-theory symmetry to-write-about to-simulate</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e1017af743d1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:probability-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-simulate"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1701.09175">
    <title>[1701.09175] Skip Connections as Effective Symmetry-Breaking</title>
    <dc:date>2017-02-16T11:42:13+00:00</dc:date>
    <link>https://arxiv.org/abs/1701.09175</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Skip connections made the training of very deep neural networks possible and have become an indispendable component in a variety of neural architectures. A completely satisfactory explanation for their success remains elusive. Here, we present a novel explanation for the benefits of skip connections in training very deep neural networks. We argue that skip connections help break symmetries inherent in the loss landscapes of deep networks, leading to drastically simplified landscapes. In particular, skip connections between adjacent layers in a multilayer network break the permutation symmetry of nodes in a given layer, and the recently proposed DenseNet architecture, where each layer projects skip connections to every layer above it, also breaks the rescaling symmetry of connectivity matrices between different layers. This hypothesis is supported by evidence from a toy model with binary weights and from experiments with fully-connected networks suggesting (i) that skip connections do not necessarily improve training unless they help break symmetries and (ii) that alternative ways of breaking the symmetries also lead to significant performance improvements in training deep networks, hence there is nothing special about skip connections in this respect. We find, however, that skip connections confer additional benefits over and above symmetry-breaking, such as the ability to deal effectively with the vanishing gradients problem.
]]></description>
<dc:subject>neural-networks learning fitness-landscapes engineering-design rather-interesting symmetry nudge-targets consider:looking-to-see</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:0bd91546add8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:neural-networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:fitness-landscapes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:looking-to-see"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1611.05971">
    <title>[1611.05971] To Find the Symmetry Plane in Any Dimension, Reflect, Register, and Compute a -1 Eigenvector</title>
    <dc:date>2017-01-07T23:47:10+00:00</dc:date>
    <link>https://arxiv.org/abs/1611.05971</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[In this paper, we demonstrate that the problem of fitting a plane of reflection symmetry to data in any dimension can be reduced to the problem of registering two datasets, and that the exactness of the solution depends on the accuracy of the registration. The pipeline for symmetry plane detection consists of (1) reflecting the data with respect to an arbitrary plane, (2) registering the original and reflected datasets, and (3) finding the eigenvector of eigenvalue -1 of a matrix given by the reflection and registration mappings. Results are shown for 2D and 3D datasets. We discuss in detail a particular biological application in which we study the 3D symmetry of manual myelinated neuron reconstructions throughout the body of a larval zebrafish that were extracted from serial-section electron micrographs. The data consists of curves that are represented as sequences of points in 3D, and there are two goals: first, find the plane of mirror symmetry given that the neuron reconstructions are nearly symmetric; second, find pairings of symmetric curves.
]]></description>
<dc:subject>image-processing symmetry rather-odd algorithms to-understand seems-straightforward-enough</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d3cfd2724e08/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-odd"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-understand"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:seems-straightforward-enough"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.cgl.uwaterloo.ca/csk/projects/">
    <title>The Craig Web Experience: Projects</title>
    <dc:date>2016-12-18T16:02:14+00:00</dc:date>
    <link>http://www.cgl.uwaterloo.ca/csk/projects/</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Projects]]></description>
<dc:subject>projects computational-geometry algorithms geometry symmetry to-write-about mathematical-recreations papers</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:e4e5624b8563/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:projects"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:to-write-about"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:papers"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1507.02762">
    <title>[1507.02762] A Quasilinear-Time Algorithm for Tiling the Plane Isohedrally with a Polyomino</title>
    <dc:date>2016-04-12T12:45:21+00:00</dc:date>
    <link>http://arxiv.org/abs/1507.02762</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[A plane tiling consisting of congruent copies of a shape is isohedral provided that for any pair of copies, there exists a symmetry of the tiling mapping one copy to the other. We give a O(nlog2n)-time algorithm for deciding if a polyomino with n edges can tile the plane isohedrally. This improves on the O(n18)-time algorithm of Keating and Vince and generalizes recent work by Brlek, Proven\c{c}al, F\'{e}dou, and the second author.
]]></description>
<dc:subject>tiling group-theory symmetry rather-interesting proof computational-geometry nudge-targets consider:rediscovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:397946a7c1d3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:proof"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rediscovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1506.08518">
    <title>[1506.08518] Fast Computation of Abelian Runs</title>
    <dc:date>2015-11-03T12:38:00+00:00</dc:date>
    <link>http://arxiv.org/abs/1506.08518</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Given a word w and a Parikh vector , an abelian run of period  in w is a maximal occurrence of a substring of w having abelian period . Our main result is an online algorithm that, given a word w of length n over an alphabet of cardinality σ and a Parikh vector , returns all the abelian runs of period  in w in time O(n) and space O(σ+p), where p is the norm of , i.e., the sum of its components. We also present an online algorithm that computes all the abelian runs with periods of norm p in w in time O(np), for any given norm p. Finally, we give an O(n2)-time offline randomized algorithm for computing all the abelian runs of w. Its deterministic counterpart runs in O(n2logσ) time.
]]></description>
<dc:subject>strings group-theory algorithms symmetry rather-interesting combinatorics enumeration classification nudge-targets consider:feature-discovery</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7e25d982bcb6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:strings"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:enumeration"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:feature-discovery"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1411.3647">
    <title>[1411.3647] The infinite cyclohedron and its automorphism group</title>
    <dc:date>2015-09-22T22:02:03+00:00</dc:date>
    <link>http://arxiv.org/abs/1411.3647</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Cyclohedra are a well-known infinite familiy of finite-dimensional polytopes that can be constructed from centrally symmetric triangulations of even-sided polygons. In this article we introduce an infinite-dimensional analogue and prove that the group of symmetries of our construction is a semidirect product of a degree 2 central extension of Thompson's infinite finitely presented simple group T with the cyclic group of order 2. These results are inspired by a similar recent analysis by the first author of the automorphism group of an infinite-dimensional associahedron.
]]></description>
<dc:subject>group-theory symmetry combinatorics rather-interesting lovely nudge-targets consider:find-something-I-don't-know</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:741530ecd258/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:lovely"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:find-something-I-don't-know"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1507.08374">
    <title>[1507.08374] Characterization and Construction of a Family of Highly Symmetric Spherical Polyhedra with Application in Modeling Self-Assembling Structures</title>
    <dc:date>2015-08-22T14:56:50+00:00</dc:date>
    <link>http://arxiv.org/abs/1507.08374</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass domes. However, they only represent a small number of possible spherical layouts which can serve as templates for symmetric assembly. In this paper, we formalize the necessary and sufficient conditions for symmetric assembly using exactly one type of building block. All such assemblies correspond to spherical polyhedra which are edge-transitive and face-transitive, but not necessarily vertex-transitive. This describes a new class of polyhedra outside of the well-studied Platonic, Archimedean, Catalan and and Johnson solids. We show that this new family, dubbed almost-regular polyhedra, can be pa- rameterized using only two variables and provide an efficient algorithm to generate an infinite series of such polyhedra. Additionally, considering the almost-regular polyhedra as templates for the assembly of 3D spherical shell structures, we developed an efficient polynomial time shell assembly approximation algorithm for an otherwise NP-hard geometric optimization problem.
]]></description>
<dc:subject>computational-geometry geometry engineering-design symmetry rather-interesting nudge-targets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:d8f429d94642/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:engineering-design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1504.06823">
    <title>[1504.06823] An Algebraic Realization of the Taylor-Socolar Aperiodic Monotilings</title>
    <dc:date>2015-07-19T12:44:41+00:00</dc:date>
    <link>http://arxiv.org/abs/1504.06823</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The first aperiodic monotiling, introduced by Taylor, was based on a trapezoidal prototile equipped with 14 distinct decorations. A presentation of the closely related Taylor-Socolar aperiodic monotiling is based on a hexagonal prototile equipped with 7 decorations. This paper gives decoration-free algebraic descriptions equivalent to each of these presentations. It also shows how the monotilings and Taylor triangles pattern that characterizes the aperiodicity can be obtained from just one algebraic equation.
]]></description>
<dc:subject>tiling aperiodic-tiling geometry symmetry rather-interesting rewriting-systems nudge-targets consider:rediscovery consider:performance-measures how-would-you-evolve-aperiodic-tilings?</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:a8897f949b6b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aperiodic-tiling"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rewriting-systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rediscovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:performance-measures"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:how-would-you-evolve-aperiodic-tilings?"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1502.03792">
    <title>[1502.03792] Counting toroidal binary arrays, II</title>
    <dc:date>2015-03-09T11:24:59+00:00</dc:date>
    <link>http://arxiv.org/abs/1502.03792</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We derive formulas for (i) the number of toroidal n×n binary arrays, allowing rotation of rows and/or columns as well as matrix transposition, and (ii) the number of toroidal n×n binary arrays, allowing rotation and/or reflection of rows and/or columns as well as matrix transposition.
]]></description>
<dc:subject>combinatorics counting group-theory symmetry nudge-targets consider:rediscovery consider:representation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:dd62edddfe1c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:combinatorics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:counting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rediscovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1501.01891">
    <title>[1501.01891] From art to geometry: aesthetic and beauty in the learning process</title>
    <dc:date>2015-02-01T22:43:02+00:00</dc:date>
    <link>http://arxiv.org/abs/1501.01891</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Starting from the concept that knowledge comes as element of mediation between the convergent thinking, founded on experience, and the divergent thinking, placed in the perceptive, intuitive, creative dimension, in this paper we want to present an idea for developing an educational path combining the concept of beauty and some historical notes. It is possible to use this dissertation as a starting point to conceive a geometric laboratory that drawing inspiration from artistic works, get to create geometric shapes provided with fascinating symmetries
]]></description>
<dc:subject>symmetry aesthetics generative-art rather-interesting psychology learning-by-doing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:75a36b47c2cf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:aesthetics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:generative-art"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:rather-interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:psychology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:learning-by-doing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1404.0948">
    <title>[1404.0948] The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes</title>
    <dc:date>2015-01-19T11:35:44+00:00</dc:date>
    <link>http://arxiv.org/abs/1404.0948</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[Previous work identifying depth-optimal n-channel sorting networks for 9≤n≤16 is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper revisits the problem of generating two-layer prefixes modulo symmetries. An improved notion of symmetry is provided and a novel technique based on regular languages and graph isomorphism is shown to generate the set of non-symmetric representations. An empirical evaluation demonstrates that the new method outperforms the generate-and-test approach by orders of magnitude and easily scales until n=40.
]]></description>
<dc:subject>sorting optimization group-theory symmetry you-keep-using-that-word it's-counterintuitive-they-say nudge-targets consider:representation consider:rule-discovery-as-such</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:f3e4cb89847e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:sorting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:you-keep-using-that-word"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:it's-counterintuitive-they-say"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:representation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:consider:rule-discovery-as-such"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1407.0224">
    <title>[1407.0224] Concentric Symmetry</title>
    <dc:date>2014-07-12T21:41:25+00:00</dc:date>
    <link>http://arxiv.org/abs/1407.0224</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[The quantification of symmetries in complex networks is typically done globally in terms of automorphisms. In this work we focus on local symmetries around nodes, which we call connectivity patterns. We develop two topological transformations that allow a concise characterization of the different types of symmetry appearing on networks and apply these concepts to six network models, namely the Erd\H{o}s-R\'enyi, Barab\'asi-Albert, random geometric graph, Waxman, Voronoi and rewired Voronoi models. Real-world networks, namely the scientific areas of Wikipedia, the world-wide airport network and the street networks of Oldenburg and San Joaquin, are also analyzed in terms of the proposed symmetry measurements. Several interesting results, including the high symmetry exhibited by the Erd\H{o}s-R\'enyi model, are observed and discussed.
]]></description>
<dc:subject>via:cshalizi graph-theory symmetry network-theory stamp-collecting feature-extraction nudge-targets interesting</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:fb52b8e1a5dc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:via:cshalizi"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:graph-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:network-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:stamp-collecting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:feature-extraction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:interesting"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1403.6637">
    <title>[1403.6637] Probably Approximately Symmetric: Fast 3D Symmetry Detection with Global Guarantees</title>
    <dc:date>2014-04-19T11:42:19+00:00</dc:date>
    <link>http://arxiv.org/abs/1403.6637</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA[We present a fast algorithm for global 3D symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with an overwhelming probability. Our method uses a carefully designed sampling of the transformation space, where each transformation is efficiently evaluated using a property testing technique. We prove that the density of the sampling depends on the total variation of the shape, allowing us to derive formal bounds on the algorithm's complexity and approximation quality. We further investigate different volumetric shape representations (in the form of truncated distance transforms), and in such a way control the total variation of the shape and hence the sampling density and the runtime of the algorithm. A comprehensive set of experiments assesses the proposed method, including an evaluation on the eight categories of the COSEG data-set. This is the first large-scale evaluation of any symmetry detection technique that we are aware of.
]]></description>
<dc:subject>image-processing classification detectors machine-learning symmetry interesting nudge-targets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:3a2f41183f13/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:image-processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:classification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:detectors"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:machine-learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:interesting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1207.6452">
    <title>[1207.6452] A New Rose : The First Simple Symmetric 11-Venn Diagram</title>
    <dc:date>2012-08-12T11:17:48+00:00</dc:date>
    <link>http://arxiv.org/abs/1207.6452</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA["A symmetric Venn diagram is one that is invariant under rotation, up to a relabeling of curves. A simple Venn diagram is one in which at most two curves intersect at any point. In this paper we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to crosscut symmetry we found many simple symmetric Venn diagrams with 11 curves. This answers an existence question that has been open since the 1960's. The first such diagram that was discovered is shown here."]]></description>
<dc:subject>Venn-diagram set-theory visualization optimization symmetry nudge-targets</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:Vaguery/b:7a17263e0456/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:Venn-diagram"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:set-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:visualization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1007.2460">
    <title>[1007.2460] Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry</title>
    <dc:date>2010-07-28T13:08:51+00:00</dc:date>
    <link>http://arxiv.org/abs/1007.2460</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA["We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with symmetry groups p3m1, p4m, or p6m that have polyominoes or polyiamonds as fundamental domains. We display the algorithms' output and give enumeration tables for small values of n.…"
]]></description>
<dc:subject>computational-geometry algorithms mathematical-recreations group-theory symmetry nudge-targets tiling</dc:subject>
<dc:identifier>https://pinboard.in/u:Vaguery/b:108d34c17af7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:computational-geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:algorithms"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:mathematical-recreations"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:group-theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nudge-targets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:tiling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.zwoje-scrolls.com/zwoje44/text23.htm">
    <title>Zwoje (The Scrolls) 44, 2006</title>
    <dc:date>2009-07-02T13:57:36+00:00</dc:date>
    <link>http://www.zwoje-scrolls.com/zwoje44/text23.htm</link>
    <dc:creator>Vaguery</dc:creator><description><![CDATA["The proposition of the paper is that a direct relation held between the spatial shape of the church, its dedication and the cultural and political situation in the region. These churches inspire further studies of the use of the equilateral triangle plan in architecture, particularly for sacred buildings. In the future such studies should result in a more complete review and perhaps a full catalogue of buildings established on such a plan."
]]></description>
<dc:subject>architecture design symmetry churches nanohistory</dc:subject>
<dc:identifier>https://pinboard.in/u:Vaguery/b:6e72a6b81586/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:architecture"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:design"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:symmetry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:churches"/>
	<rdf:li rdf:resource="https://pinboard.in/u:Vaguery/t:nanohistory"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>