https://pinboard.in/u:Vaguery/public/ recent bookmarks from Vaguery 2026-06-12T12:11:33+00:00 https://arxiv.org/abs/2406.19562 Vagueryλ(w) for all vertices w in the neighborhood of v. The pinnacle set of (G,λ) contains all the pinnacles of the labeled graph. A subset S⊆[n] is a pinnacle set of G if there exists a labeling λ such that S is the pinnacle set of (G,λ). Of interest to us is the question: Which subsets of [n] are the pinnacle sets of G? Our main results are as follows. We show that when G is connected, G has a size-k pinnacle set if and only if G has an independent set of the same size. Consequently, determining if G has a size-k pinnacle set and determining if G has a particular subset S as a pinnacle set are NP-complete problems. Nonetheless, we completely identify all the pinnacle sets of complete graphs, complete bipartite graphs, cycles and paths. We also present two techniques for deriving new pinnacle sets from old ones that imply a typical graph has many pinnacle sets. Finally, we define a poset on all the size-k pinnacle sets of G and show that it is a join semilattice. If, additionally, the poset has a minimum element, then it is a distributive lattice. We conclude with some open problems for further study. ]]> combinatorics fitness-landscapes peak-counting enumeration to-write-about to-cite loads-more-refs-needed https://pinboard.in/ https://pinboard.in/u:Vaguery/b:3f066a26b922/ 2026-05-24T17:22:15+00:00 https://hal.science/tel-05570783v1 Vaguery mathematical-recreations combinatorics book rather-interesting RNA-folding philosophy-of-science looking-to-see https://pinboard.in/ https://pinboard.in/u:Vaguery/b:9c46af2bec6a/ 2026-05-24T16:19:14+00:00 https://arxiv.org/abs/2604.12392 Vaguery combinatorics enumeration polyominoes counting discrete-mathematics Catalan-numbers representation rather-interesting https://pinboard.in/ https://pinboard.in/u:Vaguery/b:e41074f25cbc/ 2026-05-24T10:53:42+00:00 https://arxiv.org/abs/2408.06691 Vaguery nonlinear-dynamics cellular-automata ergodic-systems combinatorics complexology rather-interesting classification to-write-about to-simulate https://pinboard.in/ https://pinboard.in/u:Vaguery/b:163a69784c1b/ 2026-05-24T10:47:17+00:00 https://arxiv.org/abs/2407.11632 Vaguery2j. These permutations define the wiggly lattice, an induced sublattice of the weak order. We then prove that the wiggly complex is isomorphic to the boundary complex of the polar of the wigglyhedron, for which we give explicit and simple vertex and facet descriptions. Interestingly, we observe that any Cambrian associahedron is normally equivalent to a well-chosen face of the wigglyhedron. Finally, we recall the correspondence of wiggly arcs with objects in a category, and we develop categorical criteria for a subset of wiggly arcs to form a face of the wiggly complex. ]]> category-theory combinatorics enumeration mathematical-recreations rather-interesting to-write-about to-visualize https://pinboard.in/ https://pinboard.in/u:Vaguery/b:c6f72fa24635/ 2026-05-22T11:20:50+00:00 https://arxiv.org/abs/2502.12717 Vaguery machine-learning mathematical-programming combinatorics neural-networks formal-languages to-understand to-write-about group-theory rather-interesting feature-construction approximation https://pinboard.in/ https://pinboard.in/u:Vaguery/b:062e950d111d/ 2026-05-22T10:22:03+00:00 https://arxiv.org/abs/2605.22129 Vaguery topology combinatorics mathematical-recreations mathematics knot-theory to-understand enumeration consider:structural-dynamics https://pinboard.in/ https://pinboard.in/u:Vaguery/b:67c9f5ce3c4c/ 2026-04-20T15:54:44+00:00 https://arxiv.org/abs/2502.08188 Vaguery self-organization self-assembly packing molecular-design looking-to-see physics! rather-interesting colloids combinatorics https://pinboard.in/ https://pinboard.in/u:Vaguery/b:2386898a5462/ 2026-02-20T13:53:19+00:00 https://arxiv.org/abs/2405.08532 Vaguery discrepancy permutations combinatorics symbolic-dynamics to-understand to-simulate consider:higher-order-substrings algorithms probability-theory https://pinboard.in/ https://pinboard.in/u:Vaguery/b:37b92b01207d/ 2025-11-01T20:38:15+00:00 https://arxiv.org/abs/2508.16441 Vaguery number-theory rewriting-systems nonlinear-dynamics rather-interesting continued-fractions computational-dynamics to-understand to-write-about consider:visualization fractals combinatorics https://pinboard.in/ https://pinboard.in/u:Vaguery/b:88b271621dbf/ 2025-06-25T19:22:27+00:00 https://users.mccme.ru/smirnoff/papers/friezes-eng.pdf Vaguery mathematical-recreations mathematics John-Conway combinatorics rather-interesting to-understand number-theory enumeration https://pinboard.in/ https://pinboard.in/u:Vaguery/b:561a22e0c563/ 2025-04-16T19:09:10+00:00 https://arxiv.org/abs/math/9801088 Vaguery geometry enumeration combinatorics classics amazing-papers to-write-about to-simulate consider:squares https://pinboard.in/ https://pinboard.in/u:Vaguery/b:ffcbd8d7924e/ 2025-04-16T13:38:33+00:00 https://arxiv.org/abs/2204.13501 Vaguery scheduling heuristics looking-to-see rather-interesting combinatorics planning periodic-solutions geometry-of-search purdy-pitchers https://pinboard.in/ https://pinboard.in/u:Vaguery/b:0d35ecee5f6e/ 2024-12-21T17:43:43+00:00 https://arxiv.org/abs/2407.11533 Vaguery low-discrepancy-samples algorithms numerical-methods approximation rather-interesting to-write-about to-simulate combinatorics https://pinboard.in/ https://pinboard.in/u:Vaguery/b:1f07890f97e1/ 2024-11-03T16:06:28+00:00 https://arxiv.org/abs/2307.14011 Vaguery tiling aperiodic-tiling rather-interesting mathematical-recreations to-simulate combinatorics https://pinboard.in/ https://pinboard.in/u:Vaguery/b:ff68fca26cd6/ 2024-10-28T12:58:30+00:00 https://arxiv.org/abs/2203.08856 Vaguery aperiodic-tiling tiling combinatorics plane-geometry rather-interesting to-understand rewriting-systems consider:animation consider:visualization https://pinboard.in/ https://pinboard.in/u:Vaguery/b:a005f34a88fe/ 2024-10-28T12:54:11+00:00 https://arxiv.org/abs/2206.01276 Vaguery packing physics probability-theory combinatorics to-understand representation to-simulate consider:looking-to-see consider:animation https://pinboard.in/ https://pinboard.in/u:Vaguery/b:2d5e7b086932/ 2024-10-08T19:24:42+00:00 https://dspace.cuni.cz/handle/20.500.11956/193142 Vaguery parking-functions combinatorics methodological-moves generalization rather-interesting to-write-about to-automate nudge-targets consider:classification open-problems https://pinboard.in/ https://pinboard.in/u:Vaguery/b:000159c37683/ 2024-09-20T15:29:59+00:00 https://bookstore.ams.org/view?ProductCode=PSPUM/110 Vaguery combinatorics open-problems AMS to-read want https://pinboard.in/ https://pinboard.in/u:Vaguery/b:8ecf6c857226/ 2024-09-08T15:23:21+00:00 https://arxiv.org/abs/2112.12197 Vaguery algorithmic-information-theory AIT computational-complexity looking-to-see rather-interesting halting-problem enumeration combinatorics to-understand consider:FFX consider:not-worrying https://pinboard.in/ https://pinboard.in/u:Vaguery/b:872641e819d6/ 2024-09-05T01:03:26+00:00 https://arxiv.org/abs/2212.11644 Vaguery sorting combinatorics graph-theory matrices construction rather-interesting to-understand enumeration consider:lexicase consider:multiobjective-sets consider:probability-theory https://pinboard.in/ https://pinboard.in/u:Vaguery/b:0d7d0ee327b3/ 2024-08-31T16:32:44+00:00 https://arxiv.org/abs/2403.03280 Vaguery combinatorics permutations rather-interesting parking-functions to-write-about to-simulate consider:sampling nudge-targets https://pinboard.in/ https://pinboard.in/u:Vaguery/b:d5378b7fb701/ 2024-07-23T12:31:38+00:00 https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf Vaguery open-problems mathematical-recreations mathematics to-write-about consider:benchmarks number-theory combinatorics review collection https://pinboard.in/ https://pinboard.in/u:Vaguery/b:6079ad3d87f0/ 2024-07-21T14:26:27+00:00 https://arxiv.org/abs/2303.06524v4 Vaguery2, one can ask for the size of the largest CD, thus finding the largest CDs provides an important benchmark for heuristic-based combinatorial optimisation algorithms. Despite extensive research over the past three decades, the CD sizes identified in 1996 remain the best known for many values of n. When n>8, conducting an exhaustive search becomes computationally unfeasible, thereby prompting the use of heuristic methods. To address this, we developed a novel heuristic search algorithm in which a specially designed heuristic function, backed by a lookup database, directs the search towards promising branches in the search tree. Our algorithm found new large CDs of size 1082 (surpassing the previous record of 1069) for n=10, and 2349 (improving the previous 2324) for n=11. Notably, these newly discovered CDs exhibit characteristics distinct from those of known CDs.]]> permutations combinatorics metaheuristics rather-interesting looking-to-see enumeration to-write-about to-simulate https://pinboard.in/ https://pinboard.in/u:Vaguery/b:1bbab28907e4/ 2024-07-21T14:15:55+00:00 https://arxiv.org/abs/2404.01597 Vaguery permutations combinatorics enumeration rather-interesting patterns to-write-about nudge-targets https://pinboard.in/ https://pinboard.in/u:Vaguery/b:e0127eba92f5/ 2024-07-20T15:51:44+00:00 https://arxiv.org/abs/2203.01669 Vaguery models rather-interesting combinatorics molecular-design chemistry data-structures abstraction to-write-about to-simulate https://pinboard.in/ https://pinboard.in/u:Vaguery/b:a1db5f12a14f/ 2024-07-03T10:12:26+00:00 https://arxiv.org/abs/2206.13877 Vaguery combinatorics permutations rather-interesting to-write-about consider:push-and-trees consider:stack-languages https://pinboard.in/ https://pinboard.in/u:Vaguery/b:e5f4d50593a9/ 2024-07-02T10:56:36+00:00 https://arxiv.org/abs/2310.12687 Vaguery combinatorics group-theory symmetry enumeration rather-interesting trees to-write-about consider:mutation-operators consider:rewriting-systems consider:coverage https://pinboard.in/ https://pinboard.in/u:Vaguery/b:8b207808104e/ 2023-09-21T10:20:03+00:00 https://arxiv.org/abs/2002.03705 Vaguery mathematical-recreations number-theory rather-interesting combinatorics constraint-satisfaction heuristics to-write-about to-visualize consider:arbitrary-relationships https://pinboard.in/ https://pinboard.in/u:Vaguery/b:9a2ab2704299/ 2023-09-02T15:18:45+00:00 https://arxiv.org/abs/2308.15317 Vaguery packing combinatorics computational-geometry looking-to-see rather-interesting enumeration to-write-about nudge-targets https://pinboard.in/ https://pinboard.in/u:Vaguery/b:2d4362d8197e/ 2023-08-22T13:26:51+00:00 https://arxiv.org/abs/2307.03525 Vaguery computational-geometry combinatorics enumeration packing rather-interesting to-visualize consider:isomorphism nudge-targets https://pinboard.in/ https://pinboard.in/u:Vaguery/b:9b8c12db5757/ 2023-08-22T13:23:48+00:00 https://arxiv.org/abs/2308.08970 Vaguery graph-theory classification rather-interesting generative-models enumeration combinatorics nudge-targets consider:classification to-write-about https://pinboard.in/ https://pinboard.in/u:Vaguery/b:74624b80c3f9/ 2023-06-27T12:34:48+00:00 https://arxiv.org/abs/2012.03187 Vaguery0, where e1,e2,⋯,ek is the standard basis of ℝk. We define the maximum size of a k-dimensional corner-free subset of {1,2,⋯,N}k by ck(N). In this paper, we show that the number of k-dimensional corner-free subsets of the k-dimensional grid {1,2,⋯,N}k is at most 2O(ck(N)) for infinitely many values of N. Our main tool for the proof is a supersaturation result for k-dimensional corners in sets of size Θ(ck(N)) and the hypergraph container method. ]]> rather-interesting combinatorics open-questions set-theory hypergraphs enumeration consider:finders consider:classification https://pinboard.in/ https://pinboard.in/u:Vaguery/b:c588fb637308/ 2023-05-16T11:04:31+00:00 https://arxiv.org/abs/2305.01774 Vaguery tiling enumeration rather-interesting combinatorics to-write-about to-simulate consider:near-misses consider:visualization https://pinboard.in/ https://pinboard.in/u:Vaguery/b:a760e99732e6/ 2022-12-05T11:25:54+00:00 https://blog.tanyakhovanova.com/2022/03/fun-with-latin-squares/ Vaguery mathematical-recreations latin-suqares combinatorics constraint-satisfaction rather-interesting to-write-about consider:abstract-moves consider:general-chieces https://pinboard.in/ https://pinboard.in/u:Vaguery/b:9574d906e290/ 2022-09-28T10:20:06+00:00 https://arxiv.org/abs/2206.10003 Vaguery combinatorics domino-tiling enumeration symmetry representation to-understand to-simulate consider:moves-as-text-transformations https://pinboard.in/ https://pinboard.in/u:Vaguery/b:41aba0acbdfd/ 2022-08-24T16:16:27+00:00 https://arxiv.org/abs/1904.05573 Vaguery combinatorics enumeration number-theory rather-interesting constraint-satisfaction to-understand to-write-about consider:visualization https://pinboard.in/ https://pinboard.in/u:Vaguery/b:852fab24d57f/ 2022-07-24T12:30:43+00:00 https://arxiv.org/abs/1606.02982 Vaguery random-walks enumeration combinatorics rather-interesting OEIS generating-functions discrete-mathematics to-understand to-write-about consider:rediscovery https://pinboard.in/ https://pinboard.in/u:Vaguery/b:cdecdeb4cb27/ 2022-07-11T10:48:38+00:00 https://www.futilitycloset.com/2022/01/26/extra-magic/ Vaguery magic-squares combinatorics constraint-satisfaction mathematical-recreations rather-interesting polyominoes to-understand reference? https://pinboard.in/ https://pinboard.in/u:Vaguery/b:2af70eb40c87/ 2022-05-22T12:59:16+00:00 https://divisbyzero.com/2022/01/27/preorders-and-finite-topological-spaces/ Vaguery set-theory combinatorics rather-interesting enumeration explanation discrete-mathematics https://pinboard.in/ https://pinboard.in/u:Vaguery/b:49ae06dc764a/ 2022-05-04T12:56:11+00:00 https://arxiv.org/abs/1202.0664 Vaguery game-theory combinatorics to-understand computation consider:wth https://pinboard.in/ https://pinboard.in/u:Vaguery/b:5ec73d42f4da/ 2022-05-04T12:54:07+00:00 https://arxiv.org/abs/1104.3049 Vaguery game-theory combinatorics planning decision-making optimization to-understand to-write-about consider:simulation https://pinboard.in/ https://pinboard.in/u:Vaguery/b:01eebcbf3a24/ 2022-05-04T12:51:05+00:00 https://arxiv.org/abs/0912.0448 Vaguery game-theory category-theory combinatorics to-understand representation algebra https://pinboard.in/ https://pinboard.in/u:Vaguery/b:f1981291c1af/ 2022-03-12T13:08:54+00:00 https://arxiv.org/abs/2201.04888 Vaguery review graph-theory random-graphs rather-interesting algorithms combinatorics sampling to-write-about to-visualize https://pinboard.in/ https://pinboard.in/u:Vaguery/b:10e6ca326168/ 2022-03-12T13:04:45+00:00 https://arxiv.org/abs/1905.04490 Vaguery graph-theory rewriting-systems rather-interesting combinatorics random-graphs network-theory to-understand to-write-about to-simulate https://pinboard.in/ https://pinboard.in/u:Vaguery/b:e077ff5346e5/ 2022-03-12T12:52:53+00:00 https://arxiv.org/abs/1805.04991 Vaguery hypergraphs enumeration combinatorics set-theory rather-interesting consider:these-trasitional-moves to-visualize consider:animation https://pinboard.in/ https://pinboard.in/u:Vaguery/b:603d26a848b7/ 2022-03-12T12:48:49+00:00 https://arxiv.org/abs/1805.07217 Vaguery tiling enumeration combinatorics spherical-geometry to-write-about to-visualize consider:interactive-app https://pinboard.in/ https://pinboard.in/u:Vaguery/b:580ea9c68e4a/ 2022-03-11T11:31:01+00:00 https://arxiv.org/abs/2002.02376 Vaguery constraint-satisfaction artificial-intelligence solvers rather-interesting combinatorics to-write-about to-embed consider:Wordle-and-so-on https://pinboard.in/ https://pinboard.in/u:Vaguery/b:36cef7daa153/ 2022-03-06T11:38:36+00:00 https://arxiv.org/abs/1708.08975 Vaguery hypergraphs graph-coloring set-theory combinatorics proof rather-interesting to-write-about to-visualize consider:sampling https://pinboard.in/ https://pinboard.in/u:Vaguery/b:045f357f81c9/ 2022-03-05T11:29:05+00:00 https://arxiv.org/abs/2010.05666 Vaguery hypergraphs combinatorics graph-coloring rather-interesting define-your-terms good-backgrounder to-write-about to-visualize consider:diagrams https://pinboard.in/ https://pinboard.in/u:Vaguery/b:503c8f92b48d/ 2022-02-28T14:03:37+00:00 https://arxiv.org/abs/1708.05223 Vaguery information-theory signal-processing signal-to-noise combinatorics rather-interesting to-write-about to-simulate https://pinboard.in/ https://pinboard.in/u:Vaguery/b:a8e32de4ab65/ 2022-02-20T13:53:22+00:00 https://arxiv.org/abs/1909.12419 Vaguery combinatorics mathematical-recreations enumeration rather-interesting representation board-games https://pinboard.in/ https://pinboard.in/u:Vaguery/b:7dc5953284b9/ 2022-02-06T14:09:49+00:00 https://arxiv.org/abs/2101.07608 Vaguery game-theory number-theory combinatorics partitions to-understand review meta-combinatorics rather-interesting https://pinboard.in/ https://pinboard.in/u:Vaguery/b:81e1157045d6/ 2022-01-31T13:43:41+00:00 https://arxiv.org/abs/2103.15850 Vaguery number-theory combinatorics rather-interesting proof mathematical-recreations to-write-about nudge-targets consider:classifying-a-set consider:feature-discovery https://pinboard.in/ https://pinboard.in/u:Vaguery/b:f907cc06ed49/ 2022-01-29T12:31:50+00:00 https://arxiv.org/abs/2107.10318 Vaguery combinatorics probability-theory rather-interesting plane-geometry constraint-satisfaction number-theory all-kinds-of-stuff-really to-write-about to-understand OEIS https://pinboard.in/ https://pinboard.in/u:Vaguery/b:9999dc880227/ 2022-01-27T11:56:55+00:00 https://arxiv.org/abs/2010.11100 Vaguery geometric-graphs hypergraphs combinatorics enumeration rather-interesting limited-cases to-write-about to-visualize consider:sampling consider:distributions consider:estimating https://pinboard.in/ https://pinboard.in/u:Vaguery/b:02fda276c259/ 2022-01-24T14:01:29+00:00 https://arxiv.org/abs/2109.14777 Vaguery dimension-reduction experimental-design rather-interesting combinatorics algorithms polynomials enumeration to-write-about to-visualize consider:random-sampling https://pinboard.in/ https://pinboard.in/u:Vaguery/b:549f4020ab59/ 2022-01-24T12:31:32+00:00 https://arxiv.org/abs/1801.01288 Vaguery enumeration combinatorics probability-theory rather-interesting to-write-about to-simulate consider:visualization consider:sampling-methods https://pinboard.in/ https://pinboard.in/u:Vaguery/b:e443746bbcee/ 2022-01-23T12:32:36+00:00 https://arxiv.org/abs/1011.6195 Vaguery combinatorics enumeration rather-interesting to-simulate to-write-about consider:visualization https://pinboard.in/ https://pinboard.in/u:Vaguery/b:b3d41e7abb1b/ 2022-01-14T13:13:49+00:00 https://arxiv.org/abs/1805.03863 Vaguery combinatorics enumeration rather-interesting review discrete-mathematics feature-construction to-write-about consider:equivalences consider:group-theory https://pinboard.in/ https://pinboard.in/u:Vaguery/b:2c0d3c8e737c/ 2022-01-02T21:24:09+00:00 https://arxiv.org/abs/1906.06069 Vaguery computational-methods combinatorics enumeration representation rather-interesting to-understand to-write-about consider:S-expressions consider:algebraic-simplification https://pinboard.in/ https://pinboard.in/u:Vaguery/b:2e9ef103e118/ 2022-01-01T13:52:09+00:00 https://arxiv.org/abs/2105.11431 Vaguery combinatorics constraint-satisfaction mathematical-recreations proof to-write-about consider:guessing to-visualize https://pinboard.in/ https://pinboard.in/u:Vaguery/b:a8a2c3e3200b/ 2022-01-01T13:41:35+00:00 https://arxiv.org/abs/1910.02662 Vaguery combinatorics number-theory open-questions representation continued-fractions permutations to-understand to-write-about consider:looking-to-see https://pinboard.in/ https://pinboard.in/u:Vaguery/b:5794c86291aa/ 2022-01-01T13:36:39+00:00 https://arxiv.org/abs/2006.14070 Vaguery combinatorics number-theory head-exploding-emoji to-understand to-write-about to-simulate consider:metaheuristics https://pinboard.in/ https://pinboard.in/u:Vaguery/b:f5d99cc2ff26/ 2021-12-19T12:45:52+00:00 https://arxiv.org/abs/2109.14774 Vaguery permutations patterns combinatorics rather-interesting to-understand feature-construction constraint-satisfaction https://pinboard.in/ https://pinboard.in/u:Vaguery/b:5bd999267590/ 2021-12-19T12:36:35+00:00 https://arxiv.org/abs/2107.06188 Vaguery symmetry combinatorics rather-interesting feature-construction group-theory strings to-understand to-write-about consider:code https://pinboard.in/ https://pinboard.in/u:Vaguery/b:497a7b1767d6/ 2021-11-16T10:27:29+00:00 https://arxiv.org/abs/2106.01190 Vaguery strings combinatorics enumeration algorithms rather-interesting to-write-about consider:implementation consider:concentration https://pinboard.in/ https://pinboard.in/u:Vaguery/b:2e21349d14e5/ 2021-11-04T12:56:40+00:00 https://arxiv.org/abs/1704.00212 Vaguery combinatorics graph-rewriting enumeration rather-interesting to-visualize to-simulate https://pinboard.in/ https://pinboard.in/u:Vaguery/b:8d23dbd0258b/ 2021-11-04T12:51:00+00:00 https://arxiv.org/abs/1701.08787 Vaguery network-theory robustness security combinatorics feature-construction to-simulate to-write-about https://pinboard.in/ https://pinboard.in/u:Vaguery/b:6d8a6eb2d889/ 2021-10-30T01:19:54+00:00 https://arxiv.org/abs/2107.10167 Vaguery combinatorics self-assembly rather-interesting rather-odd magnets mathematical-recreations enumeration to-write-about to-visualize consider:forbidden-patterns consider:rarity https://pinboard.in/ https://pinboard.in/u:Vaguery/b:41dab87f2b12/