Results 61 to 70 of about 14,274 (218)
Representation theory methods in extremal combinatorics
, 2016 The research of this thesis lies in the area of extremal combinatorics. The word "extremal" comes from the kind of problems that are studied in this field. In fact, if a collection of finite objects (numbers, subsets, subspaces, graphs, etc.) satisfies some restrictions then the following questions are of interest from the perspective of extremal ...
Rafael Plaza
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Counting Independent Sets in Percolated Graphs via the Ising Model
Random Structures &Algorithms, Volume 68, Issue 1, January 2026.ABSTRACT Given a graph G$$ G $$, we form a random subgraph Gp$$ {G}_p $$ by including each edge of G$$ G $$ independently with probability p$$ p $$. We provide an asymptotic expansion of the expected number of independent sets in random subgraphs of regular bipartite graphs satisfying certain vertex‐isoperimetric properties, extending the work of ...
Anna Geisler +3 more
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Beyond sum-free sets in the natural numbers [PDF]
, 2014 For an interval [1,N]⊆N, sets S⊆[1,N] with the property that |{(x,y)∈S2:x+y∈S}|=0, known as sum-free sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)=|{(x,y)∈S2:x+y∈S}|, and analyze its behaviour ...
Huczynska, Sophie
core
The Necessary Uniformity of Physical Probability
Philosophy and Phenomenological Research, Volume 112, Issue 1, Page 290-306, January 2026.ABSTRACT According to contemporary consensus, physical probabilities may be “non‐uniform”: they need not correspond to a uniform measure over the space of physically possible worlds. Against consensus, I argue that only uniform probabilities connect robustly to long‐run frequencies.
Ezra Rubenstein
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Kneser graphs are like Swiss cheese
Discrete Analysis, 2018 Kneser graphs are like Swiss cheese, Discrete Analysis 2018:2, 18 pp. This paper relates two very interesting areas of research in extremal combinatorics: removal lemmas, and influence of variables.
Ehud Friedgut, Oded Regev
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Integer colorings with forbidden rainbow sums
, 2020 For a set of positive integers $A \subseteq [n]$, an $r$-coloring of $A$ is rainbow sum-free if it contains no rainbow Schur triple. In this paper we initiate the study of the rainbow Erd\H{o}s-Rothchild problem in the context of sum-free sets, which ...
Cheng, Yangyang +4 more
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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Hamilton cycles in graphs and hypergraphs: an extremal perspective [PDF]
, 2014 As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion and quasi ...
Kühn, Daniela, Osthus, Deryk
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Extremal Combinatorics in Geometry and Graph Theory
, 2013 We study a problem in extremal geometry posed by Paul Erdos and George Szekeres in 1935. This problem is to find the smallest positive integer N(n) such that every point set in general position (no three on a line) of N(n) points contains the vertex set of a convex n-gon.
Jonathan E. Beagley
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On certain extremal Banach–Mazur distances and Ader's characterization of distance ellipsoids
Mathematika, Volume 72, Issue 1, January 2026.Abstract A classical consequence of the John Ellipsoid Theorem is the upper bound n$\sqrt {n}$ on the Banach–Mazur distance between the Euclidean ball and any symmetric convex body in Rn$\mathbb {R}^n$. Equality is attained for the parallelotope and the cross‐polytope. While it is known that they are unique with this property for n=2$n=2$ but not for n⩾
Florian Grundbacher, Tomasz Kobos
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