Realizations of the Associahedron and Cyclohedron
Realizations of the Associahedron and Cyclohedron
复制标题
联合面体和环面体的实现
DOI：
10.1007/s00454-007-1319-6
复制
发表时间：
2005
影响因子：
0.8
通讯作者：
C. Lange
中科院分区：
文献类型：
--
作者：
Christophe Hohlweg;C. Lange
我们描述了许多不同的实现与整数坐标的associahedron（即Stasheff多面体）和为多面体（即Bott-Taubes多面体），并比较它们与置换面体的类型A和B，分别。坐标是通过一种算法获得的，该算法使用An或Bn型的定向Coxeter图作为唯一的输入数据，并且专用于J. L.一个人的某个方向。所描述的实现具有作为正常扇的A型和B型寒武纪扇。这解决了N的一个猜想。这些类型寒武纪晶格的阅读。
We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them with the permutahedron of type A and B, respectively. The coordinates are obtained by an algorithm which uses an oriented Coxeter graph of type An or Bn as the only input data and which specializes to a procedure presented by J.-L. Loday for a certain orientation of An. The described realizations have cambrian fans of type A and B as normal fans. This settles a conjecture of N. Reading for cambrian lattices of these types.