TY - JOUR
T1 - Spectra of hypergraphs and applications
AU - Feng, Keqin
AU - Li, Wen Ch ing Winnie
N1 - Funding Information:
-Research supported in part by National Science Foundation Grant RII90-03126, National Security Agency Grant MDA904-92-H-3054, and a grant from National Science Concil in Taiwan.
Funding Information:
* Research supported in part by a grant from the National Natural Science Foundation of China.
PY - 1996/9
Y1 - 1996/9
N2 - To a regular hypergraph we attach an operator, called its adjacency matrix, and study the second largest eigenvalue as well as the overall distribution of the spectrum of this operator. Our definition and results extend naturally what is known for graphs, including the analogous threshold bound 2 √k - 1 for k-regular graphs. As an application of our results, we obtain asymptotic behavior, as N tends to infinity, of the dimension of the space generated by classical cusp forms of weight 2 level N and trivial character which are eigenfunctions of a fixed Hecke operator Tp with integral eigenvalues.
AB - To a regular hypergraph we attach an operator, called its adjacency matrix, and study the second largest eigenvalue as well as the overall distribution of the spectrum of this operator. Our definition and results extend naturally what is known for graphs, including the analogous threshold bound 2 √k - 1 for k-regular graphs. As an application of our results, we obtain asymptotic behavior, as N tends to infinity, of the dimension of the space generated by classical cusp forms of weight 2 level N and trivial character which are eigenfunctions of a fixed Hecke operator Tp with integral eigenvalues.
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U2 - 10.1006/jnth.1996.0109
DO - 10.1006/jnth.1996.0109
M3 - Article
AN - SCOPUS:0030243382
SN - 0022-314X
VL - 60
SP - 1
EP - 22
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -