Extension to the Beraha-Kahane-Weiss Theorem with Applications

TL;DR

This paper extends the Beraha-Kahane-Weiss theorem to a broader class of functions, enabling new applications in graph theory and combinatorics, particularly in analyzing roots of graph polynomials.

Contribution

The paper generalizes the BKW theorem to more functions and demonstrates its utility in combinatorial applications.

Findings

Extended BKW theorem to new classes of functions

Applied the extended theorem to combinatorial problems

Provided new insights into roots of graph polynomials

Abstract

The beautiful Beraha-Kahane-Weiss theorem has found many applications within graph theory, allowing for the determination of the limits of root of graph polynomials in settings as vast as chromatic polynomials, network reliability, and generating polynomials related to independence and domination. Here we extend the class of functions to which the BKW theorem can be applied, and provide some applications in combinatorics.