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Mark Gritter<p>"Unfolding Boxes with Local Constraints" by Long Qian, Eric Wang, Bernardo Subercaseaux, and Marijn J. H. Heule <a href="https://arxiv.org/abs/2506.01079" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2506.01079</span><span class="invisible"></span></a></p><p>"We consider the problem of finding and enumerating polyominos that can be folded into multiple non-isomorphic boxes. ... In this work, we propose a new SAT-based approach that replaces these global constraints with simple local constraints that have substantially better propagation properties. Our approach dramatically improves the scalability of both computing and enumerating common box unfoldings: (i) while previous approaches could only find common unfoldings of two boxes up to area 88, ours easily scales beyond 150, and (ii) while previous approaches were only able to enumerate common unfoldings up to area 30, ours scales up to 60. This allows us to rule out 46, 54, and 58 as the smallest areas allowing a common unfolding of three boxes, thereby refuting a conjecture of Xu et al. (2017)"</p><p>Source code available, I was able to run it and find an example of a common mesh for 11x1x1 and 5x3x1 in a couple minutes. Very impressive!</p><p><a href="https://github.com/LongQianQL/CADE30-BoxUnfoldings" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">github.com/LongQianQL/CADE30-B</span><span class="invisible">oxUnfoldings</span></a></p><p><a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/folding" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>folding</span></a></p>
Dan Drake 🦆<p>So my research area in math is combinatorics, and my name is Drake...so how on earth did I not discover "Discrete Mathematics With Ducks" by sarah-marie belcastro until just now??! 🤔🦆</p><p><a href="http://www.toroidalsnark.net/dmwd.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">http://www.</span><span class="">toroidalsnark.net/dmwd.html</span><span class="invisible"></span></a></p><p>I need that book.</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/books" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>books</span></a> <a href="https://mathstodon.xyz/tags/discretemath" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>discretemath</span></a> <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/ducks" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ducks</span></a></p>
Hacker News<p>Maypole Dance of Braid Like Groups</p><p><a href="https://divisbyzero.com/2009/05/04/the-maypole-braid-group/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">divisbyzero.com/2009/05/04/the</span><span class="invisible">-maypole-braid-group/</span></a></p><p><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HackerNews</span></a> <a href="https://mastodon.social/tags/Maypole" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Maypole</span></a> <a href="https://mastodon.social/tags/Dance" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Dance</span></a> <a href="https://mastodon.social/tags/Braid" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Braid</span></a> <a href="https://mastodon.social/tags/Groups" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Groups</span></a> <a href="https://mastodon.social/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://mastodon.social/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Combinatorics</span></a> <a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HackerNews</span></a></p>
Ross Kang<p>Just yesterday, I was musing to a (younger) research visitor, "I hope that within my lifetime we will still see another breakthrough on the bounds for R(3,k)"...</p><p><a href="https://arxiv.org/abs/2505.13371" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2505.13371</span><span class="invisible"></span></a></p><p>I am excited to see what developments follow on from here!</p><p>(Also that old adage: just as soon as you publish a survey (<a href="https://arxiv.org/abs/2501.03379" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2501.03379</span><span class="invisible"></span></a>) it is out of date.)</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/ExtremalCombinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ExtremalCombinatorics</span></a> <a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>probability</span></a></p>
ƧƿѦςɛ♏ѦਹѤʞ<p><span class="h-card" translate="no"><a href="https://fosstodon.org/@catselbow" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>catselbow</span></a></span> <br>Astonishing! I hadn't come across this before - absolutely fascinating!<br><a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mastodon.social/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mastodon.social/tags/polynomial" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>polynomial</span></a> <a href="https://mastodon.social/tags/polynomials" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>polynomials</span></a> <a href="https://mastodon.social/tags/CatalanNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CatalanNumbers</span></a> <a href="https://mastodon.social/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mastodon.social/tags/Galois" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Galois</span></a> <a href="https://mastodon.social/tags/GaloisTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GaloisTheory</span></a> <br><a href="https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">tandfonline.com/doi/epdf/10.10</span><span class="invisible">80/00029890.2025.2460966?needAccess=true</span></a></p>
Bornach<p>Meta's Llama 4 (which is being forced on all <a href="https://masto.ai/tags/WhatsApp" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WhatsApp</span></a> users) doesn't do any of chain-of-thought reasoning and incorrectly calculates the number of squares of one colour. Claims that a 7x7 checker board with one corner missing has 23 of one colour so makes tiling impossible but then continues on for several paragraphs about possible tiling approaches.</p><p><a href="https://masto.ai/tags/Llama4" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Llama4</span></a> <a href="https://masto.ai/tags/MetaAI" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MetaAI</span></a> <a href="https://masto.ai/tags/AIhype" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AIhype</span></a> <a href="https://masto.ai/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://masto.ai/tags/puzzle" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>puzzle</span></a> <a href="https://masto.ai/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a></p>
Charlotte Aten<p>A fundamental result in universal algebra is the Subdirect Representation Theorem, which tells us how to decompose an algebra \(A\) into its "basic parts". Formally, we say that \(A\) is a subdirect product of \(A_1\), \(A_2\), ..., \(A_n\) when \(A\) is a subalgebra of the product<br>\[<br> A_1\times A_2\times\cdots\times A_n<br>\]<br>and for each index \(1\le i\le n\) we have for the projection \(\pi_i\) that \(\pi_i(A)=A_i\). In other words, a subdirect product "uses each component completely", but may be smaller than the full product.</p><p>A trivial circumstance is that \(\pi_i:A\to A_i\) is an isomorphism for some \(i\). The remaining components would then be superfluous. If an algebra \(A\) has the property than any way of representing it as a subdirect product is trivial in this sense, we say that \(A\) is "subdirectly irreducible".</p><p>Subdirectly irreducible algebras generalize simple algebras. Subdirectly irreducible groups include all simple groups, as well as the cyclic \(p\)-groups \(\mathbb{Z}_{p^n}\) and the Prüfer groups \(\mathbb{Z}_{p^\infty}\).</p><p>In the case of lattices, there is no known classification of the finite subdirectly irreducible (or simple) lattices. This page (<a href="https://math.chapman.edu/~jipsen/posets/si_lattices92.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">math.chapman.edu/~jipsen/poset</span><span class="invisible">s/si_lattices92.html</span></a>) by Peter Jipsen has diagrams showing the 92 different nontrivial subdirectly irreducible lattices of order at most 8. See any patterns?</p><p>We know that every finite subdirectly irreducible lattice can be extended to a simple lattice by adding at most two new elements (Lemma 2.3 from Grätzer's "The Congruences of a Finite Lattice", <a href="https://arxiv.org/pdf/2104.06539" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/pdf/2104.06539</span><span class="invisible"></span></a>), so there must be oodles of finite simple lattices out there.</p><p><a href="https://mathstodon.xyz/tags/UniversalAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>UniversalAlgebra</span></a> <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>logic</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/algebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>algebra</span></a> <a href="https://mathstodon.xyz/tags/AbstractAlgebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AbstractAlgebra</span></a></p>
Matthew Turland<p>Your <a href="https://phpc.social/tags/DnD" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DnD</span></a> Party is Too Big<br><a href="https://youtube.com/watch?v=0pc9Uf3vFDU&amp;si=N2Dor4X31i93IGie" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">youtube.com/watch?v=0pc9Uf3vFD</span><span class="invisible">U&amp;si=N2Dor4X31i93IGie</span></a></p><p><a href="https://phpc.social/tags/DungeonsAndDragons" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DungeonsAndDragons</span></a> <a href="https://phpc.social/tags/TTRPGs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TTRPGs</span></a> <a href="https://phpc.social/tags/Scheduling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Scheduling</span></a> <a href="https://phpc.social/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Combinatorics</span></a> <a href="https://phpc.social/tags/Statistics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Statistics</span></a> <a href="https://phpc.social/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://phpc.social/tags/Adulting" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Adulting</span></a></p>
claude<p>searching for any structures / theory that involve a particular operation on non-empty lists of postitive integers like "the length of the list multiplied by the least common multiple of all the items in the list"</p><p>any ideas? references to any literature would be very appreciated if you know of any.</p><p><a href="https://post.lurk.org/tags/askfedi" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>askfedi</span></a> <a href="https://post.lurk.org/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://post.lurk.org/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://post.lurk.org/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://post.lurk.org/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://post.lurk.org/tags/GroupTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GroupTheory</span></a> <a href="https://post.lurk.org/tags/DiscreteMath" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DiscreteMath</span></a></p>
Dan Drake 🦆<p>1/2 </p><p>I want to find a particular sequence of permutations. The requirements are:</p><p>* you start with the identity<br>* each permutation differs from the next by a permutation with only adjacent transpositions<br>* each number appears in every position at least once.</p><p>For example, for $n = 4$, here's an example:</p><p>1234,2143,2413,4231,4321,3412 </p><p>What's the shortest such sequence as a function of $n$?</p><p>I have one algorithm that produces such a sequence that is length $2n +2$ for even $n$, and $2n-1$ for odd $n$. The attached photo should make the algorithm clear. But I don't have a good proof that this is optimal.</p><p>This is related to some <a href="https://mathstodon.xyz/tags/crochet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>crochet</span></a> I'm working on, surprisingly enough.</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a></p>
Stuart Spence<p>"How Anime Fans Stumbled upon a Mathematical Proof: When a fan of a cult anime series wanted to watch its episodes in every possible order, they asked a question that had perplexed combinatorial mathematicians for years."</p><p><a href="https://mstdn.ca/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mstdn.ca/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mstdn.ca/tags/anime" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>anime</span></a> <a href="https://mstdn.ca/tags/4chan" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>4chan</span></a> <a href="https://mstdn.ca/tags/compsci" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>compsci</span></a> <a href="https://mstdn.ca/tags/computerscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>computerscience</span></a> </p><p><a href="https://www.scientificamerican.com/article/the-surprisingly-difficult-mathematical-proof-that-anime-fans-helped-solve/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">scientificamerican.com/article</span><span class="invisible">/the-surprisingly-difficult-mathematical-proof-that-anime-fans-helped-solve/</span></a></p>
Ross Kang<p>A question for the (combinatorial) hive mind.</p><p>There are a lot of extremal results that are matched asymptotically by some probabilistic construction, but with some gap, often quite substantial. I'm thinking about the Ramsey numbers R(k,k) or R(3,k), but examples of this phenomenon are prevalent.</p><p>I'm curious, does someone out there know of good examples of (extremal) results where some probabilistic construction (e.g. via a random graph) is matched asymptotically, and very precisely?</p><p><a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a></p>
Bornach<p>Gemini 2.0 Flash Thinking is really messed up for the 5x5 tiling question. Pulls numbers out of the air and justifies them by saying the calculation "is very complex"</p><p>Surprisingly its answer for the 3x3 is also incorrect. There should be 4 distinct tiling patterns.<br><a href="https://masto.ai/tags/AI" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AI</span></a> <a href="https://masto.ai/tags/mathsodon" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathsodon</span></a> <a href="https://masto.ai/tags/GenerativeAI" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GenerativeAI</span></a> <a href="https://masto.ai/tags/AIslop" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AIslop</span></a> <a href="https://masto.ai/tags/ArtificialIntelligence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ArtificialIntelligence</span></a> <a href="https://masto.ai/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://masto.ai/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://masto.ai/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://masto.ai/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a></p>
Ross Kang<p>Starting out in mathematical research, especially in discrete mathematics, a big focus is problem-solving. It's like a race, and once you've solved one, you set out right away for the next adrenaline rush.</p><p>Take for granted a bustling market of open problems (again, especially in discrete mathematics). Scour papers or problem sites. Challenge close colleagues with the ones that eluded you. The harder, the better, right? There is occasionally awkward coffee talk of that intangible `taste' or `judgement', but, come on, less talk and more solving!</p><p>(please imagine here a subtly ironic tone in my voice)</p><p>(1/3)</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <br><a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <br><a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <br><a href="https://mathstodon.xyz/tags/ExtremalCombinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ExtremalCombinatorics</span></a></p>
Ross Kang<p>A post of <span class="h-card" translate="no"><a href="https://mathstodon.xyz/@11011110" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>11011110</span></a></span> has reminded me that (after a year and a half lurking here) it's never too late for me to toot and pin an intro here.</p><p>I am a Canadian mathematician in the Netherlands, and I have been based at the University of Amsterdam since 2022. I also have some rich and longstanding ties to the UK, France, and Japan.</p><p>My interests are somewhere in the nexus of Combinatorics, Probability, and Algorithms. Specifically, I like graph colouring, random graphs, and probabilistic/extremal combinatorics. I have an appreciation for randomised algorithms, graph structure theory, and discrete geometry.</p><p>Around 2020, I began taking a more active role in the community, especially in efforts towards improved fairness and openness in science. I am proud to be part of a team that founded the journal, Innovations in Graph Theory (<a href="https://igt.centre-mersenne.org/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">igt.centre-mersenne.org/</span><span class="invisible"></span></a>), that launched in 2023. (That is probably the main reason I joined mathstodon!) I have also been a coordinator since 2020 of the informal research network, A Sparse (Graphs) Coalition (<a href="https://sparse-graphs.mimuw.edu.pl/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">sparse-graphs.mimuw.edu.pl/</span><span class="invisible"></span></a>), devoted to online collaborative workshops. In 2024, I helped spearhead the MathOA Diamond Open Access Stimulus Fund (<a href="https://www.mathoa.org/diamond-open-access-stimulus-fund/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">mathoa.org/diamond-open-access</span><span class="invisible">-stimulus-fund/</span></a>).</p><p>Until now, my posts have mostly been about scientific publishing and combinatorics.</p><p><a href="https://mathstodon.xyz/tags/introduction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>introduction</span></a> <br><a href="https://mathstodon.xyz/tags/openscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>openscience</span></a> <br><a href="https://mathstodon.xyz/tags/diamondopenaccess" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>diamondopenaccess</span></a> <br><a href="https://mathstodon.xyz/tags/scientificpublishing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>scientificpublishing</span></a> <br><a href="https://mathstodon.xyz/tags/openaccess" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>openaccess</span></a> <br><a href="https://mathstodon.xyz/tags/RemoteConferences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>RemoteConferences</span></a> <br><a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <br><a href="https://mathstodon.xyz/tags/graphtheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphtheory</span></a> <br><a href="https://mathstodon.xyz/tags/ExtremalCombinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ExtremalCombinatorics</span></a> <br><a href="https://mathstodon.xyz/tags/probability" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>probability</span></a></p>
Christ van Willegen<p>I'm busy writing a <a href="https://mastodon.nl/tags/Python" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Python</span></a> program that creates (virtual) <a href="https://mastodon.nl/tags/Lego" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Lego</span></a> <a href="https://mastodon.nl/tags/moc" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>moc</span></a> files for <a href="https://mastodon.nl/tags/LEOCad" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LEOCad</span></a>. But, I've hit a <a href="https://mastodon.nl/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> wall, and my <a href="https://mastodon.nl/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a>-fu fails me here...</p><p>Are/is there any <a href="https://mastodon.nl/tags/programmer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>programmer</span></a> and/or <a href="https://mastodon.nl/tags/mathematician" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematician</span></a> who can help me? </p><p>See picture for what I'm trying to do...</p>
Jon Awbrey<p>Riffs and Rotes • Happy New Year 2025<br>• <a href="https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/01</span><span class="invisible">/01/riffs-and-rotes-happy-new-year-2025/</span></a></p><p>\( \text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}. \)</p><p>\( \text{Then} ~ 2025<br>= 81 \cdot 25<br>= 3^4 5^2 \)</p><p>\( = {p_2}^4 {p_3}^2<br>= {p_2}^{{p_1}^{p_1}} {p_3}^{p_1}<br>= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_2}}^{p_1}<br>= {p_{p_1}}^{{p_1}^{p_1}} {p_{p_{p_1}}}^{p_1} \)</p><p>No information is lost by dropping the terminal 1s. Thus we may write the following form.</p><p>\[ 2025 = {p_p}^{p^p} {p_{p_p}}^p \]</p><p>The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.</p><p>Riff 2025<br>• <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.files.wordp</span><span class="invisible">ress.com/2025/01/riff-2025.png</span></a></p><p>Rote 2025<br>• <a href="https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.files.wordp</span><span class="invisible">ress.com/2025/01/rote-2025.png</span></a></p><p>Reference —</p><p>Riffs and Rotes<br>• <a href="https://oeis.org/wiki/Riffs_and_Rotes" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">oeis.org/wiki/Riffs_and_Rotes</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/Arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Arithmetic</span></a> <a href="https://mathstodon.xyz/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Combinatorics</span></a> <a href="https://mathstodon.xyz/tags/Computation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computation</span></a> <a href="https://mathstodon.xyz/tags/Factorization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Factorization</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a> <a href="https://mathstodon.xyz/tags/GroupTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GroupTheory</span></a> <br><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/Primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Primes</span></a> <a href="https://mathstodon.xyz/tags/Recursion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Recursion</span></a> <a href="https://mathstodon.xyz/tags/Representation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Representation</span></a> <a href="https://mathstodon.xyz/tags/RiffsAndRotes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>RiffsAndRotes</span></a></p>
Ross Kang<p>(via Vic Reiner)</p><p>An article by Ann Schilling on Diamond OA journals in combinatorics, and in particular the genesis of the journal Combinatorial Theory:</p><p><a href="https://www.ams.org/journals/notices/202501/noti3040/noti3040.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">ams.org/journals/notices/20250</span><span class="invisible">1/noti3040/noti3040.html</span></a></p><p><a href="https://mathstodon.xyz/tags/diamondopenaccess" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>diamondopenaccess</span></a> <a href="https://mathstodon.xyz/tags/openaccess" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>openaccess</span></a> <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/scientificpublishing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>scientificpublishing</span></a></p>
2something<p><span>New account, new introduction!<br><br>I'm Beth. I'm a queer mathematician who loves musical theater, webcomics, teaching math, and my cat. <br><br>Favorite areas of math: Topology, geometry, and combinatorics.<br><br>Favorite musicals: Chess, Into the Woods, Next to Normal, Sunday in the Park With George, Sweeney Todd<br><br>Favorite webcomics: this is long enough to get its own post:<br></span><a href="https://transfem.social/notes/a1ryogrga5qu00g9" rel="nofollow noopener" target="_blank">https://transfem.social/notes/a1ryogrga5qu00g9</a><span><br><br></span><a href="https://transfem.social/tags/Introduction" rel="nofollow noopener" target="_blank">#Introduction</a> <a href="https://transfem.social/tags/Queer" rel="nofollow noopener" target="_blank">#Queer</a> <a href="https://transfem.social/tags/Mathematician" rel="nofollow noopener" target="_blank">#Mathematician</a> <a href="https://transfem.social/tags/Math" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://transfem.social/tags/Musicals" rel="nofollow noopener" target="_blank">#Musicals</a> <a href="https://transfem.social/tags/MusicalTheater" rel="nofollow noopener" target="_blank">#MusicalTheater</a> <a href="https://transfem.social/tags/MusicalTheatre" rel="nofollow noopener" target="_blank">#MusicalTheatre</a> <a href="https://transfem.social/tags/Webcomics" rel="nofollow noopener" target="_blank">#Webcomics</a> <a href="https://transfem.social/tags/Teaching" rel="nofollow noopener" target="_blank">#Teaching</a> <a href="https://transfem.social/tags/TeachingMath" rel="nofollow noopener" target="_blank">#TeachingMath</a> <a href="https://transfem.social/tags/Cat" rel="nofollow noopener" target="_blank">#Cat</a> <a href="https://transfem.social/tags/Cats" rel="nofollow noopener" target="_blank">#Cats</a> <a href="https://transfem.social/tags/SillyGoose" rel="nofollow noopener" target="_blank">#SillyGoose</a> <a href="https://transfem.social/tags/Topology" rel="nofollow noopener" target="_blank">#Topology</a> <a href="https://transfem.social/tags/Geometry" rel="nofollow noopener" target="_blank">#Geometry</a> <a href="https://transfem.social/tags/Combinatorics" rel="nofollow noopener" target="_blank">#Combinatorics</a> <a href="https://transfem.social/tags/Chess" rel="nofollow noopener" target="_blank">#Chess</a> <a href="https://transfem.social/tags/ChessTheMusical" rel="nofollow noopener" target="_blank">#ChessTheMusical</a> <a href="https://transfem.social/tags/IntoTheWoods" rel="nofollow noopener" target="_blank">#IntoTheWoods</a> <a href="https://transfem.social/tags/NextToNormal" rel="nofollow noopener" target="_blank">#NextToNormal</a> <a href="https://transfem.social/tags/SundayInTheParkWithGeorge" rel="nofollow noopener" target="_blank">#SundayInTheParkWithGeorge</a> <a href="https://transfem.social/tags/SweeneyTodd" rel="nofollow noopener" target="_blank">#SweeneyTodd</a> <a href="https://transfem.social/tags/PandorasTaleWiki" rel="nofollow noopener" target="_blank">#PandorasTaleWiki</a> <a href="https://transfem.social/tags/RainverseWiki" rel="nofollow noopener" target="_blank">#RainverseWiki</a></p>
Paul Balduf<p>During our <a href="https://mathstodon.xyz/tags/combinatorics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorics</span></a> in <a href="https://mathstodon.xyz/tags/physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>physics</span></a> online conference, we have interactively made a mindmap to connect speakers, audience, and shared topics. Besides looking funny, this has really helped me concentrate on the talks because I had to pay attention if something had been mentioned in a previous talk already. <br>A full resolution version is on my website.</p>