Coxeter submodular functions and deformations of Coxeter permutahedra
Coxeter submodular functions and deformations of Coxeter permutahedra
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DOI：
10.1016/j.aim.2020.107039
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发表时间：
2019-04
影响因子：
1.7
通讯作者：
Federico Ardila;F. Castillo;C. Eur;A. Postnikov
中科院分区：
文献类型：
--
作者：
Federico Ardila;F. Castillo;C. Eur;A. Postnikov
我们描述了一个考克斯特置换面体的变形锥，或者等价地，与考克斯特复形相关联的复曲面的nef锥。这类多面体包含重要的家庭，如重量多面体，签署图形zonotopes，考克斯特拟阵，根锥，和考克斯特associahedra。我们的描述扩展了已知的广义置换面体，多拟阵，和子模函数之间的对应关系到任何有限反射群。
We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This class of polytopes contains important families such as weight polytopes, signed graphic zonotopes, Coxeter matroids, root cones, and Coxeter associahedra. Our description extends the known correspondence between generalized permutahedra, polymatroids, and submodular functions to any finite reflection group.