文章基本信息

标题：Discrete Geometry, Algebra, and Combinatorics (Invited Talk)
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作者：Jacob Fox
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：51
页码：2:1-2:1
DOI：10.4230/LIPIcs.SoCG.2016.2
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Many problems in discrete and computational geometry can be viewed as finding patterns in graphs or hypergraphs which arise from geometry or algebra. Famous Ramsey, Turán, and Szemerédi-type results prove the existence of certain patterns in graphs and hypergraphs under mild assumptions. We survey recent results which show much stronger/larger patterns for graphs and hypergraphs that arise from geometry or algebra. We further discuss whether the stronger results in these settings are due to geometric, algebraic, combinatorial, or topological properties of the graphs.
关键词：discrete geometry; extremal combinatorics; regularity lemmas; Ramsey theory