重新审视排列-缔合面体
The permuto-associahedron revisited
摘要：
一个连接代数和几何组合学的经典问题是实现问题：给定一个偏序集，确定是否存在一个多面体，其面格是偏序集。20世纪90年代，Kapranov将偏序集定义为置换面体的面偏序集和伴随面体的面偏序集的混合，并提出了这个偏序集是否可实现的问题。在他提出这个问题后不久，雷纳和齐格勒就意识到了这一点。在前人工作的基础上，通过同时构造置换结合面体的顶点集和法扇，给出了Kapranov偏序集的一种不同实现.
英文摘要：
A classic problem connecting algebraic and geometric combinatorics is the realization problem: given a poset, determine whether there exists a polytope whose face lattice is the poset. In 1990s, Kapranov defined a poset as a hybrid between the face poset of a permutohedron and that of an associahedron, and he asked whether this poset is realizable. Shortly after his question was posed, Reiner and Ziegler provided a realization. Based on our previous work on the nested braid fan, we provide in this paper a different realization of Kapranov's poset by constructing the vertex set and the normal fan of a permuto-associahedron simultaneously.
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