Duke Mathematical Journal
- Duke Math. J.
- Volume 139, Number 1 (2007), 141-171.
Explicit construction of a Ramanujan -regular hypergraph
Abstract
Using the main properties of the skew polynomial rings 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 and with respect to a certain set of generators, over a finite field with elements
Article information
Source
Duke Math. J., Volume 139, Number 1 (2007), 141-171.
Dates
First available in Project Euclid: 13 July 2007
Permanent link to this document
https://projecteuclid.org/euclid.dmj/1184341240
Digital Object Identifier
doi:10.1215/S0012-7094-07-13913-9
Mathematical Reviews number (MathSciNet)
MR2322678
Zentralblatt MATH identifier
1180.11016
Subjects
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
Citation
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