Qué anidaedra son quitaedra
Qué anidaedra son quitaedra
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Qué anidaedra son quitaedra
DOI：
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发表时间：
2014
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通讯作者：
Vincent Pilaud
中科院分区：
文献类型：
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作者：
Vincent Pilaud
一个可移多面体是通过从经典置换面体的刻面描述中删除不等式而得到的多面体。相关的例子包括从准面体到置换面体本身，这就提出了一个自然的问题，即哪些嵌套面体可以被实现为移四面体。本文证明了在交下闭的任何连通建筑集的套复形都可以实现为一个可移四面体。我们提出了两个互补的构造：一个基于建筑树和嵌套扇，另一个基于标准单形的扩张面的Minkowski和。一般来说，这个闭合条件是充分的，但不是获得可移四面体的必要条件。相反，我们证明了一个图形建筑集的嵌套扇是一个removahedron的正常扇当且仅当图形建筑集在相交下是封闭的，这相当于相应的图是弦的（即，任何循环都会导致一个集团）。
A removahedron is a polytope obtained by deleting inequalities from the facet description of the classical permutahedron. Relevant examples range from the associahedron to the permutahedron itself, which raises the natural question to characterize which nestohedra can be realized as removahedra. In this paper, we show that the nested complex of any connected building set closed under intersection can be realized as a removahedron. We present two complementary constructions: one based on the building trees and the nested fan, and the other based on Minkowski sums of dilated faces of the standard simplex. In general, this closure condition is sufficient but not necessary to obtain removahedra. In contrast, we show that the nested fan of a graphical building set is the normal fan of a removahedron if and only if the graphical building set is closed under intersection, which is equivalent to the corresponding graph being chordful (i.e., any cycle induces a clique).