On the polymatroid Tutte polynomial

The Tutte polynomial is a well-studied invariant of matroids. The polymatroid Tutte polynomial ${\mathcal{J}}_P(x,y)$, 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 ${\mathcal{J}}_P(x,t)$ and ${\mathcal{J}}_P(t,y)$ are interpolating for any fixed real number $t\ge 1$, and then we study the coefficients of high-order terms in ${\mathcal{J}}_P(x,1)$ and ${\mathcal{J}}_P(1,y)$. These results generalize results on interior and exterior polynomials of hypergraphs.