Mixing properties and the chromatic number of ramanujan complexes

Shai Evra, Konstantin Golubev, Alexander Lubotzky

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

Ramanujan complexes are high-dimensional simplicial complexes generalizing Ramanujan graphs. A result of Oh on quantitative property (T) for Lie groups over local fields is used to deduce a Mixing Lemma for such complexes. As an application, we prove that nonpartite Ramanujan complexes have "high girth" and high-chromatic number, generalizing a well-known result about Ramanujan graphs.

Original languageEnglish (US)
Pages (from-to)11520-11548
Number of pages29
JournalInternational Mathematics Research Notices
Volume2015
Issue number22
DOIs
StatePublished - 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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