Cyclic Polytopes and Oriented Matroids
Cyclic Polytopes and Oriented Matroids
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循环多面体和定向拟阵
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
P. Duchet
中科院分区：
文献类型：
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作者：
R. Cordovil;P. Duchet
考虑由映射 ? 参数定义的实欧几里得空间 Rd 中的力矩曲线： R?Rd,t???(t) = (t, t2,? , td)。循环d-多面体Cd(t1,?,tn)是该曲线上n&d个不同点的凸包。拟阵类似物是交替定向的均匀拟阵。如果多胞体（分别为拟阵多胞体）的面晶格与 Cd (t1,? , tn) 的面晶格同构，则称为循环。我们给出了循环（拟阵）多胞体的组合和几何特征。 Gale 给出了确定 Cd (t1,? , tn) 面的简单均匀度准则。我们描述了循环多胞形顶点的可接受排序，即盖尔均匀性准则成立的顶点的线性排序。证明系统地说明了循环多胞体的定向拟阵方法。
Consider the moment curve in the real euclidean space Rddefined parametrically by the map ?: R?Rd,t???(t) = (t, t2,? , td). The cyclic d -polytopeCd (t1,? , tn) is the convex hull ofn&d different points on this curve. The matroidal analogs are the alternating oriented uniform matroids. A polytope (resp. matroid polytope) is called cyclic if its face lattice is isomorphic to that ofCd (t1,? , tn). We give combinatorial and geometrical characterizations of cyclic (matroid) polytopes. A simple evenness criterion determining the facets ofCd (t1,? , tn) was given by Gale . We characterize the admissible orderings of the vertices of the cyclic polytope, i.e., those linear orderings of the vertices for which Gale?s evenness criterion holds. Proofs give a systematic account on an oriented matroid approach to cyclic polytopes.