论文标题
通用Tutte多项式
Universal Tutte polynomial
论文作者
论文摘要
Tutte多项式是图形和成曲线的良好的不变性。我们首先将Tutte多项式从图扩展到超图，而更普遍地从矩形到多甲状管，作为两变量的多项式。我们的定义与Cameron和Fink以及Kálmán和Postnikov的先前作品有关。然后，我们定义通用Tutte多项式$ \ t_n $，它是$ n $ in $ n $ in $ 2+（2^n-1）$变量的多项式，该变量专门针对所有多肌功能的Tutte多项式（因此所有Matroids）在带有$ n $ n $元素的地面集合中。通用多项式$ \ t_n $允许三种对称性：翻译不变性，$ s_n $ invariance和duality。
The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the Tutte polynomial from graphs to hypergraphs, and more generally from matroids to polymatroids, as a two-variable polynomial. Our definition is related to previous works of Cameron and Fink and of Kálmán and Postnikov. We then define the universal Tutte polynomial $\T_n$, which is a polynomial of degree $n$ in $2+(2^n-1)$ variables that specializes to the Tutte polynomials of all polymatroids (hence all matroids) on a ground set with $n$ elements. The universal polynomial $\T_n$ admits three kinds of symmetries: translation invariance, $S_n$-invariance, and duality.
