Results 21 to 30 of about 887,124 (211)
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
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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
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Universal limit theorems in graph coloring problems with connections to extremal combinatorics [PDF]
The Annals of Applied Probability, 2017 This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with the same birthday?).
Bhaswar B. Bhattacharya +2 more
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Ramsey numbers of cycles versus general graphs
Forum of Mathematics, Sigma, 2023 The Ramsey number $R(F,H)$ is the minimum number N such that any N-vertex graph either contains a copy of F or its complement contains H. Burr in 1981 proved a pleasingly general result that, for any graph H, provided n is sufficiently large, a ...
John Haslegrave +3 more
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Term Coding for Extremal Combinatorics: Dispersion and Complexity Dichotomies [PDF]
We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optionally, \emph{non-equality constraints}). In its basic form, all variables range over a single domain, and we seek an interpretation of the function symbols that \emph{maximises}
Søren Riis
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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
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Chromatic Turán problems and a new upper bound for the Turán density of $\mathcal{K}_4^-$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider a new type of extremal hypergraph problem: given an $r$-graph $\mathcal{F}$ and an integer $k≥2$ determine the maximum number of edges in an $\mathcal{F}$-free, $k$-colourable $r$-graph on $n$ vertices.
John Talbot
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Short proofs of some extremal results [PDF]
, 2013 We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have ...
Beck +11 more
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On the quaternion projective space
Journal of Taibah University for Science, 2020 Apart from being a vital and exciting field in mathematics with interesting results, projective spaces have various applications in design theory, coding theory, physics, combinatorics, number theory and extremal combinatorial problems. In this paper, we
Y. Omar +4 more
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