论文标题
在多层tutte多项式上
On the polymatroid Tutte polynomial
论文作者
论文摘要
Tutte多项式是一个良好的成曲线不变的。由Bernardi等人引入的Polymatroid Tutte多项式$ \ MATHCAL {J} _ {p}（X，Y）$是从矩形到多肌动力的经典Tutte多项式的扩展。在本文中，我们首先证明了$ \ Mathcal {J} _ {p}（x，x，t）$和$ \ Mathcal {j} _ {p}（t，y）$在任何固定的实际数量$ t \ geq 1 $中都在插值，然后我们研究$ \ math $ \ n Math C}的高级术语。 $ \ Mathcal {J} _ {p}（1，y）$。这些结果推广了超图的内部和外部多项式。
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 $t\geq 1$, 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.
