Some Ramanujan hypergraphs associated to

Authors:
María G. Martínez, Harold M. Stark and Audrey A. Terras

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1623-1629

MSC (2000):
Primary 11T99, 11T60, 05C65, 05E15, 15A42, 20G40

DOI:
https://doi.org/10.1090/S0002-9939-00-05965-7

Published electronically:
October 31, 2000

MathSciNet review:
1814089

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We present examples of hypergraphs constructed from homogeneous spaces of finite general linear groups. These hypergraphs are constructed using an invariant analogue of a hypervolume and their spectra are analyzed to see if they are Ramanujan in the sense of W.-C. W. Li and P. Solé.

**1.**N. Biggs,*Algebraic Graph Theory*, Cambridge U. Press, Cambridge, 1974. MR**50:151****2.**F. R. K. Chung, The Laplacian of a hypergraph,*DIMACS Series in Discrete Math. and Theoretical Computer Science, Vol. 10*, AMS, Providence, 1993, pp. 21-36. MR**95c:05083****3.**K. Feng and W.-C. W. Li, Spectra of hypergraphs and applications,*J. of Number Theory, 60*(1996), 1-22. MR**97f:05128****4.**W.-C. W. Li and P. Solé, Spectra of regular graphs and hypergraphs and orthogonal polynomials,*European J. of Combinatorics, 17*(1996), 461-477. MR**97m:05180****5.**A. Lubotzky, R. Phillips, and P. Sarnak, Ramanujan hypergraphs,*Combinatorica, 8*(1988), 261-277. MR**89m:05099****6.**M. G. Martínez, The finite upper half space and related hypergraphs, J. of Number Theory, to appear.**7.**M. G. Martínez, Ph.D. Thesis, U.C.S.D., 1998.**8.**A. Terras,*Fourier Analysis on Finite Groups and Applications*, Cambridge U. Press, Cambridge, 1999. MR**2000d:11003****9.**A. Terras, Survey of spectra of Laplacians on finite symmetric spaces,*Experimental Math., 5 (1)*, (1996), 15-32. MR**97m:11154**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
11T99,
11T60,
05C65,
05E15,
15A42,
20G40

Retrieve articles in all journals with MSC (2000): 11T99, 11T60, 05C65, 05E15, 15A42, 20G40

Additional Information

**María G. Martínez**

Affiliation:
Department of Mathematics, University of Stuttgart, Stuttgart, Germany

Email:
maria@mathematik.uni-stuttgart.de

**Harold M. Stark**

Affiliation:
Department of Mathematics, University of California–San Diego, La Jolla, California 92093-0112

Email:
stark@math.ucsd.edu

**Audrey A. Terras**

Affiliation:
Department of Mathematics, University of California–San Diego, La Jolla, California 92093-0112

Email:
aterras@ucsd.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05965-7

Received by editor(s):
September 17, 1999

Published electronically:
October 31, 2000

Communicated by:
Dennis A. Hejhal

Article copyright:
© Copyright 2000
American Mathematical Society