论文信息 - Bartholdi Zeta Functions for Hypergraphs

Bartholdi Zeta Functions for Hypergraphs

Recently, Storm defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of some regular hypergraph.

Iwao Sato

[1] Motoko Kotani,et al. Jacobian Tori Associated with a Finite Graph and Its Abelian Covering Graphs , 2000, Adv. Appl. Math..

[2] D. Zeilberger,et al. A Combinatorial Proof of Bass’s Evaluations of the Ihara-Selberg Zeta Function for Graphs , 1998, math/9806037.

[3] A. Terras,et al. Zeta Functions of Finite Graphs and Coverings , 1996 .

[4] H. Bass. THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE , 1992 .

[5] T. Sunada. L-functions in geometry and some applications , 1986 .

[6] Toshikazu Sunada,et al. Fundamental groups and Laplacians , 1988 .

[7] L. Bartholdi. Counting Paths in Graphs , 2000, math/0012161.

[8] Christopher K. Storm. The Zeta Function of a Hypergraph , 2006, Electron. J. Comb..

[9] Brendan D. McKay,et al. The Distributions of the Entries of Young Tableaux , 2002, J. Comb. Theory, Ser. A.

[10] Aaron D. Jaggard. Subsequence Containment by Involutions , 2005, Electron. J. Comb..

[11] Y. Ihara. On discrete subgroups of the two by two projective linear group over p-adic fields , 1966 .

[12] K. Hashimoto. Zeta functions of finite graphs and representations of p-adic groups , 1989 .