A decomposition formula for the Bartholdi zeta function of a hypergraph covering

TL;DR

This paper extends the decomposition formula of the Bartholdi zeta function from graph coverings to hypergraph coverings, broadening the mathematical understanding of zeta functions in complex structures.

Contribution

It generalizes Mizuno and Sato's decomposition formula for Bartholdi zeta functions from graphs to hypergraphs, introducing a new theoretical framework.

Findings

Decomposition formula extended to hypergraph coverings

Mathematical framework for hypergraph zeta functions established

Potential applications in spectral graph theory and combinatorics

Abstract

It is shown by Mizuno and Sato that the Bartholdi zeta function of a covering graph is decomposed as a product of Bartholdi zeta functions of a base graph that are associated with representations. In this paper, we extend their result to the case of a hypergraph covering.