Ramanujan geometries of type &Ãn

Authors:
Donald I. Cartwright;Patrick Solé;Andrzej Zuk
Affiliations:
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia;CNRS, I3S, ESSI, route des Colles, 06 903 Sophia Antipolis, France;CNRS, UMPA, ENS Lyon, 46 allée d'Italie, F-69364 Lyon cedex 07, France
Venue:
Discrete Mathematics
Year:
2003

Citing 6
Cited 2

Tactical configurations and their generic ring

European Journal of Combinatorics
The expected capacity of concentrators

SIAM Journal on Discrete Mathematics
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q

Journal of Combinatorial Theory Series B
Ramanujan Diagrams

SIAM Journal on Discrete Mathematics
Cayley graphs: eigenvalues, expanders and random walks

Surveys in combinatorics, 1995
Spectra of regular graphs and hypergraphs and orthogonal polynomials

European Journal of Combinatorics

Explicit constructions of Ramanujan complexes of type Ad

European Journal of Combinatorics - Special issue on combinatorics and representation theory
Overlap properties of geometric expanders: extended abstract

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms

Quantified Score

Hi-index	0.05

Visualization

Abstract

We study finite graphs which are covered by the 1-skeleton of a building of type Ãn and with an extremal spectral property: they are Ãn-Ramanujan in the sense of Lubotzky. That definition is made quantitatively explicit, refined in the directed case, and a few candidates are suggested.