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15 July 2007 Explicit construction of a Ramanujan (n1,n2,,nd1)-regular hypergraph
Alireza Sarveniazi
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Duke Math. J. 139(1): 141-171 (15 July 2007). DOI: 10.1215/S0012-7094-07-13913-9

Abstract

Using the main properties of the skew polynomial rings Fqd{τ} and some related rings, we describe the explicit construction of Ramanujan hypergraphs, which are certain simplicial complexes introduced in the author's thesis [29] (see also [30]) as generalizations of Ramanujan graphs. Such hypergraphs are described in terms of Cayley graphs of various groups. We give an explicit description of our hypergraph as the Cayley graph of the groups PSLd(Fr) and PGLd(Fr) with respect to a certain set of generators, over a finite field Fr with r elements

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Alireza Sarveniazi. "Explicit construction of a Ramanujan (n1,n2,,nd1)-regular hypergraph." Duke Math. J. 139 (1) 141 - 171, 15 July 2007. https://doi.org/10.1215/S0012-7094-07-13913-9

Information

Published: 15 July 2007
First available in Project Euclid: 13 July 2007

zbMATH: 1180.11016
MathSciNet: MR2322678
Digital Object Identifier: 10.1215/S0012-7094-07-13913-9

Subjects:
Primary: 11B75 , 11F72 , 11R58 , 20F65
Secondary: 22E45 , 51E24

Rights: Copyright © 2007 Duke University Press

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Vol.139 • No. 1 • 15 July 2007
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