Matroid Polytopes and their Volumes
Matroid Polytopes and their Volumes
复制标题
DOI：
10.1007/s00454-009-9232-9
复制
发表时间：
2010-06-01
影响因子：
0.8
通讯作者：
Doker, Jeffrey
中科院分区：
文献类型：
--
作者：
Ardila, Federico;Benedetti, Carolina;Doker, Jeffrey
我们将拟阵M的拟阵多胞形P（M）表示为单形的带符号Minkowski和，并得到P（M）的体积公式。这给出了Grassmannian Gr（k，n）中任意环面轨道闭合度的组合表达式。然后，我们推导出类似的结果的独立集多面体和基本的标志拟阵多面体的M。我们的证明是基于Postnikov的广义置换面体理论的自然扩展。
We express the matroid polytope P (M) of a matroid M as a signed Minkowski sum of simplices, and obtain a formula for the volume of P (M) . This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian Gr (k,n) . We then derive analogous results for the independent set polytope and the underlying flag matroid polytope of M. Our proofs are based on a natural extension of Postnikov's theory of generalized permutohedra.