On the polymatroid Tutte polynomial

2022/07/10 by Guan, Xiaxia, Yang, Weiling, Jin, Xian'an · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.04421

Abstract

The Tutte polynomial is a well-studied invariant of matroids. The polymatroid Tutte polynomial J_P(x,y), introduced by Bernardi et al., is an extension of the classical Tutte polynomial from matroids to polymatroids P. In this paper, we first prove that J_P(x,t) and J_P(t,y) are interpolating for any fixed real number t≥ 1, and then we study the coefficients of high-order terms in J_P(x,1) and J_P(1,y). These results generalize results on interior and exterior polynomials of hypergraphs.

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• On the coefficients of interior and exterior polynomials of polymatroids

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