A Combinatorial Method for Computing Characteristic Polynomials of Starlike Hypergraphs

TL;DR

This paper introduces a combinatorial approach utilizing the Poisson formula and chip-firing game variants to compute characteristic polynomials of adjacency tensors in starlike hypergraphs, including hyperpaths and hyperstars, both recursively and explicitly.

Contribution

It presents a novel combinatorial method for calculating characteristic polynomials of adjacency tensors in starlike hypergraphs, expanding computational techniques in hypergraph spectral theory.

Findings

Provides recursive formulas for characteristic polynomials.

Explicit computation methods for hyperpaths and hyperstars.

Connects combinatorial game theory with tensor spectral analysis.

Abstract

By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the characteristic polynomials of the adjacency tensors of starlike hypergraphs including hyperpaths and hyperstars,which are given recursively and explicitly.