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Some Ramanujan hypergraphs associated to 
Author(s):
María
G.
Martínez;
Harold
M.
Stark;
Audrey
A.
Terras
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1623-1629.
MSC (2000):
Primary 11T99, 11T60, 05C65, 05E15, 15A42, 20G40
Posted:
October 31, 2000
MathSciNet review:
1814089
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Abstract:
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.
References:
- 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
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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:
10.1090/S0002-9939-00-05965-7
PII:
S 0002-9939(00)05965-7
Received by editor(s):
September 17, 1999
Posted:
October 31, 2000
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
2000,
American Mathematical Society
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