A Polynomial Invariant and Duality for Triangulations
A Polynomial Invariant and Duality for Triangulations
复制标题
三角剖分的多项式不变量和对偶性
DOI：
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发表时间：
2010
影响因子：
0.7
通讯作者：
David Renardy
中科院分区：
文献类型：
--
作者：
Vyacheslav Krushkal;David Renardy
Tutte多项式是一个经典的不变量，在组合学和统计力学中很重要。Tutte多项式的一个本质特征是平面图G的对偶性，$T_G（X，Y）={T}_{G^*}（Y，X）$，其中$G^*$表示对偶图。我们从流形拓扑的角度研究了这一特性，为高维单纯复形制定了多项式不变量。球面三角剖分的多项式对偶是亚历山大对偶的结果。
本文的主要目的是介绍和开始研究一个更一般的四元多项式的三角剖分和处理分解的定向流形。在这种情况下，多项式对偶是流形上庞加莱对偶的一个结果。在2维中，这些不变量专用于由B定义的带状图的众所周知的多项式不变量。Bollobas和O.赖尔登的多项式的例子和具体的评价进行了讨论。
The Tutte polynomial is a classical invariant, important in combinatorics and statistical mechanics. An essential feature of the Tutte polynomial is the duality for planar graphs G, $T_G(X,Y); =; {T}_{G^*}(Y,X)$ where $G^*$ denotes the dual graph. We examine this property from the perspective of manifold topology, formulating polynomial invariants for higher-dimensional simplicial complexes. Polynomial duality for triangulations of a sphere follows as a consequence of Alexander duality.
The main goal of this paper is to introduce and begin the study of a more general 4-variable polynomial for triangulations and handle decompositions of orientable manifolds. Polynomial duality in this case is a consequence of Poincare duality on manifolds. In dimension 2 these invariants specialize to the well-known polynomial invariants of ribbon graphs defined by B. Bollobas and O. Riordan. Examples and specific evaluations of the polynomials are discussed.
Temperley-Lieb 代数的 Tutte 色恒等式
影响因子：
2
作者：
Fendley P
通讯作者：
Fendley P