Root polytopes, Tutte polynomials, and a duality theorem for bipartite
Root polytopes, Tutte polynomials, and a duality theorem for bipartite
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根多面体、Tutte 多项式和二分的对偶定理
DOI：
10.1112/plms.12015
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发表时间：
2017
影响因子：
1.8
通讯作者：
Tamas Kalman and Alexander Postnikov
中科院分区：
文献类型：
--
作者：
Chen L.;Pei D. H.;Takahashi M.;Kazuhiro Kawamura and Takeshi Miura;Tamas Kalman and Alexander Postnikov
设是一个连通二部图，其色类和根多胞形.关于由导出的超图，我们证明了的内多项式等价于的Ehrhart多项式，而Ehrhart多项式又等价于的任何三角剖分的向量。当是完全二部图时，我们的结果恢复了一个著名的由Saalschütz给出的超几何恒等式.它还意味着，在Homfly多项式的一个特殊的交替链接的某些极值系数可以读出相关的弗洛尔同调群。
Letbe a connected bipartite graph with colour classesandand root polytope. Regarding the hypergraphinduced by, we prove that the interior polynomial ofis equivalent to the Ehrhart polynomial of, which in turn is equivalent to the‐vector of any triangulation of. It follows that the interior polynomials ofand its transposeagree.Whenis a complete bipartite graph, our result recovers a well‐known hypergeometric identity due to Saalschütz. It also implies that certain extremal coefficients in the Homfly polynomial of a special alternating link can be read off of an associated Floer homology group.