Recent Trends in Combinatorics
Andrew Beveridge, Jerrold R. Griggs, Leslie Hogben, Gregg Musiker, Prasad Tetali
Springer, Apr 12, 2016 - Mathematics - 778 pages
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.
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algebra algorithm antichain applications asymptotic bipartite graph Bollobás causal set cell complex chromatic number coefficients color Comb combinatorics Comput conjecture connected contains Corollary defined definition denote dimension Discrete disjoint edit distance eigenvalues elements Erd˝os example exists finite geometric given graph G Graph Theory h-vectors Hamilton cycles Hence hereditary property homology homomesy hypergraphs independent sets inequality isomorphic k-graph labeled Laplacian Lemma length Let G linear lower bound manifolds Math Mathematics matrix matroid maximum metric spaces minimum degree Moore graphs n-vertex normalized Laplacian Note number of edges obtained order ideal pairs parameters partial order partition path perfect matching permutations polynomial polytopes poset positive integers problem proof of Theorem Proposition proved random graph result rowmotion satisfies Section simplicial complex spanning trees structure subgraph subgroup subset Theorem triangulation Turán unimodal upper bound vector vertex set Wiener index