A new determinant expression of the zeta function for a hypergraph (Q2380298)

Summary: Recently, \textit{C. K. Storm} [Electron. J. Comb. 13, No. 1, Research paper R84, 26 p. (2006; Zbl 1112.05072)] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it by the Perron-Frobenius operator of a digraph and a deformation of the usual Laplacian of a graph. We present a new determinant expression for the Ihara-Selberg zeta function of a hypergraph, and give a linear algebraic proof of Storm's Theorem. Furthermore, we generalize these results to the Bartholdi zeta function of a hypergraph.