Results 1 to 10 of about 887,124 (211)
PPP-Completeness and Extremal Combinatorics [PDF]
Electron. Colloquium Comput. Complex., 2022 Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erd\H{o}s-Rado sunflower lemma.
Romain Bourneuf +4 more
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Extremal combinatorics, iterated pigeonhole arguments, and generalizations of PPP [PDF]
Information Technology Convergence and Services, 2022 We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle.
Amol Pasarkar +2 more
semanticscholar +7 more sources
High dimensional Hoffman bound and applications in extremal combinatorics [PDF]
Algebraic Combinatorics, 2022 One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of its eigenvalues. It is easily seen that the Hoffman bound is sharp on the
Yuval Filmus +2 more
semanticscholar +7 more sources
Graphical designs and extremal combinatorics [PDF]
Linear Algebra and its Applications, 2020 A graphical design is a proper subset of vertices of a graph on which many eigenfunctions of the Laplacian operator have mean value zero. In this paper, we show that extremal independent sets make extremal graphical designs, that is, a design on which the maximum possible number of eigenfunctions have mean value zero.
Konstantin Golubev
semanticscholar +7 more sources
A path forward: Tropicalization in extremal combinatorics [PDF]
Advances in Mathematics, 2022 Many important problems in extremal combinatorics can be be stated as proving a pure binomial inequality in graph homomorphism numbers, i.e., proving that hom$(H_1,G)^{a_1}\cdots$hom$(H_k,G)^{a_k}\geq$hom$(H_{k+1},G)^{a_{k+1}}\cdots$hom$(H_m,G)^{a_m}$ holds for some fixed graphs $H_1,\dots,H_m$ and all graphs $G$.
Grigoriy Blekherman, Annie Raymond
semanticscholar +5 more sources
Refuting conjectures in extremal combinatorics via linear programming [PDF]
Journal of Combinatorial Theory, Series A, 2019 We apply simple linear programming methods and an LP solver to refute a number of open conjectures in extremal combinatorics.
Adam Zsolt Wagner
semanticscholar +8 more sources
Information Inequalities via Submodularity and a Problem in Extremal Graph Theory [PDF]
Entropy, 2022 The present paper offers, in its first part, a unified approach for the derivation of families of inequalities for set functions which satisfy sub/supermodularity properties.
Igal Sason
doaj +2 more sources
Exploring implications of Trace (Inversion) formula and Artin algebras in extremal combinatorics [PDF]
Applicable Algebra in Engineering, Communication and Computing, 2023 This note is just a modest contribution to prove several classical results in Combinatorics from notions of Duality in some Artinian K -algebras (mainly through the Trace Formula), where K is a perfect field of characteristics not equal to 2.
Luis Miguel Pardo
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Fully Computer-Assisted Proofs in Extremal Combinatorics
AAAI Conference on Artificial Intelligence, 2023 We present a fully computer-assisted proof system for solving a particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful in the past, but have so far lacked a computational counterpart to ...
Olaf Parczyk +3 more
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Entropic Matroids and Their Representation [PDF]
Entropy, 2019 This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p.
Emmanuel Abbe, Sophie Spirkl
doaj +2 more sources