A moore bound for simplicial complexes

Alexander Lubotzky; Roy Meshulam

doi:10.1112/blms/bdm003

A moore bound for simplicial complexes

Alexander Lubotzky^*, Roy Meshulam

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

Let X be a d-dimensional simplicial complex with N faces of dimension d-1. Suppose that every (d-1)-face of X is contained in at least κ ≥ d + 2 faces of X, of dimension d. Extending the classical Moore bound for graphs, it is shown that X must contain a ball B of radius at most |"log _κ-d N] whose d-dimensional homology H_d(B) is non-zero. The Ramanujan complexes constructed by Lubotzky, Samuels and Vishne are used to show that this upper bound on the radius of B cannot be improved by more than a multiplicative constant factor.

Original language	English
Pages (from-to)	353-358
Number of pages	6
Journal	Bulletin of the London Mathematical Society
Volume	39
Issue number	3
DOIs	https://doi.org/10.1112/blms/bdm003
State	Published - Jun 2007

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A moore bound for simplicial complexes

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