article

Ramanujan geometries of type Ã_n

Authors:

Donald I. Cartwright,

Andrzej ZukAuthors Info & Claims

Discrete Mathematics, Volume 269, Issue 1-3

Pages 35 - 43

https://doi.org/10.1016/S0012-365X(02)00748-3

Published: 28 July 2003 Publication History

Abstract

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

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Cited By

O'Donnell RPratt K(2022)High-dimensional expanders from Chevalley groupsProceedings of the 37th Computational Complexity Conference10.4230/LIPIcs.CCC.2022.18(1-26)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2022.18
Lubotzky ASamuels BVishne U(2018)Explicit constructions of Ramanujan complexes of type AEuropean Journal of Combinatorics10.1016/j.ejc.2004.06.00726:6(965-993)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1016/j.ejc.2004.06.007
Fox JGromov MLafforgue VNaor APach JRandall D(2011)Overlap properties of geometric expandersProceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms10.5555/2133036.2133126(1188-1197)Online publication date: 23-Jan-2011
https://dl.acm.org/doi/10.5555/2133036.2133126

Index Terms

Ramanujan geometries of type Ã_n
1. Applied computing
  1. Physical sciences and engineering
    1. Mathematics and statistics
2. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Paths and connectivity problems

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cover image Discrete Mathematics

Discrete Mathematics Volume 269, Issue 1-3

28 July 2003

341 pages

ISSN:0012-365X

Issue’s Table of Contents

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 28 July 2003

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Cited By

O'Donnell RPratt K(2022)High-dimensional expanders from Chevalley groupsProceedings of the 37th Computational Complexity Conference10.4230/LIPIcs.CCC.2022.18(1-26)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2022.18
Lubotzky ASamuels BVishne U(2018)Explicit constructions of Ramanujan complexes of type AEuropean Journal of Combinatorics10.1016/j.ejc.2004.06.00726:6(965-993)Online publication date: 29-Dec-2018
https://dl.acm.org/doi/10.1016/j.ejc.2004.06.007
Fox JGromov MLafforgue VNaor APach JRandall D(2011)Overlap properties of geometric expandersProceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms10.5555/2133036.2133126(1188-1197)Online publication date: 23-Jan-2011
https://dl.acm.org/doi/10.5555/2133036.2133126

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