Results 1 to 10 of about 934 (196)

Undecidability of polynomial inequalities in weighted graph homomorphism densities

Forum of Mathematics, Sigma
Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights.
Grigoriy Blekherman, Annie Raymond, Fan Wei   +2 more
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SPERNER THEOREMS FOR UNRELATED COPIES OF POSETS AND GENERATING DISTRIBUTIVE LATTICES

Ural Mathematical Journal
For a finite poset (partially ordered set) \(U\) and a natural number \(n\), let \(S(U,n)\) denote the largest number of pairwise unrelated copies of  \(U\) in the powerset lattice (AKA subset lattice) of an \(n\)-element set.
Gábor Czédli
doaj   +1 more source

Jordan Curves: Ramsey Approach and Topology

Mathematics
We develop a topological-combinatorial framework applying classical Ramsey theory to systems of arcs connecting points on Jordan curves and their higher-dimensional analogues.
Edward Bormashenko
doaj   +1 more source

Random Fibonacci Words via Clone Schur Functions

Forum of Mathematics, Sigma
We investigate positivity and probabilistic properties arising from the Young–Fibonacci lattice $\mathbb {YF}$ , a 1-differential poset on words composed of 1’s and 2’s (Fibonacci words) and graded by the sum of the digits.
Leonid Petrov, Jeanne Scott
doaj   +1 more source

Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case

Discrete Analysis, 2017
Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case, Discrete Analysis 2017:5, 34 pp. Szemerédi's theorem, proved in 1975, asserts that for every positive integer $k$ and every $\delta>0$ there exists $n$ such that every subset
Sean Prendiville
doaj   +1 more source

Problems in extremal and probabilistic combinatorics

, 2017
In this thesis we consider some problems in extremal and probabilistic combinatorics. In Chapter 2 we determine the maximum number of induced cycles that can be contained in a graph on n ≥ n0 vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Tuza. Let Qd denote the hypercube of dimension d. Given d ≥
Morrison, N, Noel, J
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Quasirandom Cayley graphs

Discrete Analysis, 2017
Quasirandom Cayley graphs, Discrete Analysis 2017:6, 14 pp. An extremely important phenomenon in extremal combinatorics is that of _quasirandomness_: for many combinatorial structures, it is possible to identify a list of deterministic properties, each ...
David Conlon, Yufei Zhao
doaj   +1 more source

Two problems in extremal combinatorics

, 2021
In this thesis, we focus on two problems in extremal graph theory. Extremal graph theory consists of all problems related to optimizing parameters defined on graphs. The concept of ``editing'' appears in many key results and techniques in extremal graph theory, either as a means to account for error in structural results, or as a quantity to minimize ...
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Power saving for the Brown-Erdős-Sós problem

Discrete Analysis
Power saving for the Brown-Erdős-Sós problem, Discrete Analysis 2025:5, 16 pp. It has long been known that there are important connections between extremal questions concerning hypergraphs and extremal questions in additive combinatorics.
Oliver Janzer, Abhishek Methuku, Aleksa Milojević, Benny Sudakov   +3 more
doaj   +1 more source

Coloring and extremal problems in combinatorics

, 2018
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.
openaire   +3 more sources