Results 11 to 20 of about 14,970 (213)
Coloring and extremal problems in combinatorics
, 2010 Coloring problems concern partitions of structures. The classic problem of partitioning the set of integers into a finite number of pieces so that no one piece has an arithmetic progression of a fixed length was solved in 1927. Van der Waerden's Theorem shows that it is impossible to do so.
Jacob Manske
openalex +5 more sources
Extremal problems and the combinatorics of sumsets
, 2023 18 pages.
Melvyn B. Nathanson
openalex +4 more sources
Treewidth computation and extremal combinatorics [PDF]
Combinatorica, 2012 For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most n\binom{b+f}{b} such vertex subsets.
Fedor V. Fomin, Yngve Villanger
openalex +7 more sources
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
Reaction systems and extremal combinatorics properties
Theoretical Computer Science, 2015 Extremal combinatorics is the study of the size that a collection of objects must have in order to certainly satisfy a given property. Reaction systems are a recent formalism for computation inspired by chemical reactions. This work is a first contribution to the study of the behavior of large reaction systems by means of extremal combinatorics.
Alberto Dennunzio +2 more
openalex +5 more sources
Extremal combinatorics, iterated pigeonhole arguments, and generalizations of PPP
, 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. This results in the definition of a new complexity class within TFNP, which we call PLC (for "polynomial long choice ...
Amol Pasarkar +2 more
openalex +6 more sources
Optimal Probability Inequalities for Random Walks Related to Problems in Extremal Combinatorics [PDF]
SIAM Journal on Discrete Mathematics, 2012 Let S_n=X_1+...+X_n be a sum of independent symmetric random variables such that |X_{i}|\leq 1. Denote by W_n= _{1}+...+ _{n} a sum of independent random variables such that \prob{\eps_i = \pm 1} = 1/2. We prove that \mathbb{P}{S_{n} \in A} \leq \mathbb{P}{cW_k \in A}, where A is either an interval of the form [x, \infty) or just a single point.
Dainius Dzindzalieta +2 more
openalex +5 more sources
Probabilistic models for the analysis of inverse extremal problems in combinatorics [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2022 In an inverse extremal problem for a combinatorial scheme with a given value of the objective function of the form of a certain extreme value of its characteristic, a probabilistic model is developed that ensures that this value is obtained in its ...
Nataliya Yu. Enatskaya
doaj +1 more source
Exponential multivalued forbidden configurations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 The forbidden number $\mathrm{forb}(m,F)$, which denotes the maximum number of unique columns in an $m$-rowed $(0,1)$-matrix with no submatrix that is a row and column permutation of $F$, has been widely studied in extremal set theory.
Travis Dillon, Attila Sali
doaj +1 more source