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Extreme coefficients of multiplicity Tutte polynomials

Xian'an Jin, Tianlong Ma, Weiling Yang

Abstract

The multiplicity Tutte polynomial, which includes the arithmetic Tutte polynomial, is a generalization of the classical Tutte polynomial of matroids. In this paper, we obtain an expression of the general coefficient and the expressions of six extreme coefficients of multiplicity Tutte polynomials. In particular, an expression of the general coefficient and the expressions of corresponding extreme coefficients of classical Tutte polynomial of matroids are deduced.

Extreme coefficients of multiplicity Tutte polynomials

Abstract

The multiplicity Tutte polynomial, which includes the arithmetic Tutte polynomial, is a generalization of the classical Tutte polynomial of matroids. In this paper, we obtain an expression of the general coefficient and the expressions of six extreme coefficients of multiplicity Tutte polynomials. In particular, an expression of the general coefficient and the expressions of corresponding extreme coefficients of classical Tutte polynomial of matroids are deduced.
Paper Structure (5 sections, 18 theorems, 71 equations)

This paper contains 5 sections, 18 theorems, 71 equations.

Table of Contents

  1. Introduction
  2. Characteristic polynomial and related lemmas
  3. Main results
  4. Consequences
  5. Concluding remarks

Key Result

Lemma 2.1

Ellis-Monaghan Let $M$ be a matroid. Then

Theorems & Definitions (26)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Theorem 3.1
  • Theorem 3.2
  • proof
  • ...and 16 more