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arXiv · 1407.7700

Mixing properties and the chromatic number of Ramanujan complexes

Shai Evra·Konstantin Golubev·Alexander Lubotzky
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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.

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Shai Evra, Konstantin Golubev, Alexander Lubotzky. 2014-07-30. Mixing properties and the chromatic number of Ramanujan complexes. https://arxiv.org/abs/1407.7700

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