Mixing properties and the chromatic number of Ramanujan complexes
Combinatorics
2019-06-04 v2 Group Theory
Representation Theory
Abstract
Ramanujan complexes are high dimensional simplical 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 non-partite Ramanujan complexes have 'high girth' and high chromatic number, generalizing a well known result about Ramanujan graphs.
Keywords
Cite
@article{arxiv.1407.7700,
title = {Mixing properties and the chromatic number of Ramanujan complexes},
author = {Shai Evra and Konstantin Golubev and Alexander Lubotzky},
journal= {arXiv preprint arXiv:1407.7700},
year = {2019}
}