Equidecomposable and weakly neighborly polytopes
Equidecomposable and weakly neighborly polytopes
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可等分解和弱邻域多胞体
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
M. Bayer
中科院分区：
文献类型：
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作者：
M. Bayer
如果其所有三角形都具有相同的脸部数，则可以等式地复合。对于等式合成的多型，所有最小仿射依赖性都具有相等数量的正系数和负系数。一个子类由弱的邻居多面体组成，其中每组顶点包含在尺寸为集合时的面孔中最多是两倍。弱邻居多层的每个三角剖分的媒介等于多层本身的hh-vector。研究了这类多型的组合特性。弱邻居多面体的大风图以较少的顶点的特征是劳伦斯多型（Lawrence Polytopes）的已知大风图表征的精神，这是一种特殊的弱邻居多面体。
A polytope is equidecomposable if all its triangulations have the same face numbers. For an equidecomposable polytope all minimal affine dependencies have an equal number of positive and negative coefficients. A subclass consists of the weakly neighborly polytopes, those for which every set of vertices is contained in a face of at most twice the dimension as the set. Theh-vector of every triangulation of a weakly neighborly polytope equals theh-vector of the polytope itself. Combinatorial properties of this class of polytopes are studied. Gale diagrams of weakly neighborly polytopes with few vertices are characterized in the spirit of the known Gale diagram characterization of Lawrence polytopes, a special class of weakly neighborly polytopes.