Graph polynomials and Tutte-Grothendieck invariants: an application of elementary finite Fourier analysis

TL;DR

This paper explores the connections between graph polynomials, Tutte-Grothendieck invariants, and elementary finite Fourier analysis, providing new insights into their algebraic and combinatorial properties.

Contribution

It introduces a family of polynomials related to the Tutte polynomial that produce Tutte-Grothendieck invariants via finite Fourier analysis techniques.

Findings

Representation of the Tutte polynomial as a Hamming weight enumerator

Identification of a polynomial family yielding Tutte-Grothendieck invariants

Application of elementary finite Fourier analysis to graph invariants

Abstract

This paper is based on a series of talks given at the Patejdlovka Enumeration Workshop held in the Czech Republic in November 2007. The topics covered are as follows. The graph polynomial, Tutte-Grothendieck invariants, an overview of relevant elementary finite Fourier analysis, the Tutte polynomial of a graph as a Hamming weight enumerator of its set of tensions (or flows), and a description of a family of polynomials containing the graph polynomial which yield Tutte-Grothendieck invariants in a similar way.