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DTSTART;TZID=Asia/Seoul:20210616T170000
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SUMMARY:Alan Lew\, Representability and boxicity of simplicial complexes
DESCRIPTION:An interval graph is the intersection graph of a family of intervals in the real line. Motivated by problems in ecology\, Roberts defined the boxicity of a graph G to be the minimal k such that G can be written as the intersection of k interval graphs. \nA natural higher-dimensional generalization of interval graphs is the class d-representable complexes. These are simplicial complexes that carry the information on the intersection patterns of a family of convex sets in $mathbb R^d$. We define the d-boxicity of a simplicial complex X to be the minimal k such that X can be written as the intersection of k d-representable complexes. \nA classical result of Roberts\, later rediscovered by Witsenhausen\, asserts that the boxicity of a graph with n vertices is at most n/2. Our main result is the following high dimensional extension of Roberts’ theorem: Let X be a simplicial complex on n vertices with minimal non-faces of dimension at most d. Then\, the d-boxicity of X is at most $frac{1}{d+1}binom{n}{d}$. \nExamples based on Steiner systems show that our result is sharp. The proofs combine geometric and topological ideas.
URL:https://dimag.ibs.re.kr/event/2021-06-16/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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