Duke Mathematical Journal

Explicit construction of a Ramanujan (n1,n2,,nd1)-regular hypergraph

Alireza Sarveniazi

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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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Duke Math. J., Volume 139, Number 1 (2007), 141-171.

First available in Project Euclid: 13 July 2007

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Primary: 11B75: Other combinatorial number theory 11F72: Spectral theory; Selberg trace formula 11R58: Arithmetic theory of algebraic function fields [See also 14-XX] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 51E24: Buildings and the geometry of diagrams


Sarveniazi, Alireza. Explicit construction of a Ramanujan $(n_1,n_2,\ldots,n_{d-1})$ -regular hypergraph. Duke Math. J. 139 (2007), no. 1, 141--171. doi:10.1215/S0012-7094-07-13913-9. https://projecteuclid.org/euclid.dmj/1184341240

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