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

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关于多拟阵Tutte多项式

Tutte 多项式是经过充分研究的拟阵不变量。多拟阵Tutte多项式${\mathcal{时间}}_{磷}（X,y）$由 Bernardi、Kálmán 和 Postnikov 提出，是经典 Tutte 多项式从拟阵到多拟阵P的扩展。在本文中，我们首先证明${\mathcal{时间}}_{磷}（X,t）$和${\mathcal{时间}}_{磷}（t,y）$对任何固定实数进行插值$t\ge 1$，然后我们研究高阶项的系数${\mathcal{时间}}_{磷}（X,1）$和${\mathcal{时间}}_{磷}（1,y）$。这些结果概括了超图的内部和外部多项式的结果。