单邻多面体
Prodsimplicial-Neighborly Polytopes
摘要：
同时推广的邻居和邻居的立方多面体，我们介绍PSN多面体：他们的k-骨架是组合等价的产品r单纯形。我们构造PSN多面体由三种不同的方法，其中最通用的是桑亚尔和齐格勒的“投影变形产品”建设的产品的任意简单的多面体的扩展。对于一般的r和k，我们得到的最低维数是2k+r+1。使用类似的拓扑障碍引入Sanyal绑定闵可夫斯基和的顶点数，我们表明，这个维度是最小的，如果我们另外要求的PSN多面体是作为一个投影的多面体，组合等价于产品的r单纯形，当这些单纯形的尺寸都是大的相比，k。
英文摘要：
Simultaneously generalizing both neighborly and neighborly cubical polytopes, we introduce PSN polytopes: their k-skeleton is combinatorially equivalent to that of a product of r simplices. We construct PSN polytopes by three different methods, the most versatile of which is an extension of Sanyal and Ziegler's "projecting deformed products" construction to products of arbitrary simple polytopes. For general r and k, the lowest dimension we achieve is 2k+r+1. Using topological obstructions similar to those introduced by Sanyal to bound the number of vertices of Minkowski sums, we show that this dimension is minimal if we additionally require that the PSN polytope is obtained as a projection of a polytope that is combinatorially equivalent to the product of r simplices, when the dimensions of these simplices are all large compared to k.
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