Fiber Polytopes for the Projections between Cyclic Polytopes
Fiber Polytopes for the Projections between Cyclic Polytopes
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用于环状多面体之间投影的纤维多面体
DOI：
10.1006/eujc.1999.0319
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
F. Santos
中科院分区：
文献类型：
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作者：
Christos A. Athanasiadis;J. D. Loera;V. Reiner;F. Santos
循环多胞形C（n，d）是矩船体{（t，t2，. . .，td）：t？在Rd.福特？d，我们认为纤维多面体（在Billera和Sturmfels的意义上）与循环多面体的自然投影有关？C（n，d？) ? C（n，d）哪个会忘记？最后一个D？d坐标。它是已知的，这种纤维多面体有面晶格索引的连贯多面体细分的C（n，d），这是诱导的地图？.我们的主要结果刻画了三元组（n，d，d？）对于纤维多面体是典型的在以下两个意义之一：？所有的多面体细分诱导？是连贯的，？纤维多面体的结构不依赖于力矩曲线上的点的选择。我们还讨论了一个新的情况下，一个积极的答案，广义鲍斯问题，即投影？：P吗？其中Q只有规则的细分，P比它的维数多两个顶点。
The cyclic polytope C(n, d) is the convex hull of any n points on the moment curve {(t, t2, . . . , td) :t?R } in Rd. Ford?&d, we consider the fiber polytope (in the sense of Billera and Sturmfels ) associated to the natural projection of cyclic polytopes ?: C(n,d? ) ?C(n, d) which `forgets? the last d??d coordinates. It is known that this fiber polytope has face lattice indexed by the coherent polytopal subdivisions of C(n, d) which are induced by the map? . Our main result characterizes the triples (n, d, d?) for which the fiber polytope is canonical in either of the following two senses: ?all polytopal subdivisions induced by ? are coherent, ? the structure of the fiber polytope does not depend upon the choice of points on the moment curve. We also discuss a new instance with a positive answer to the generalized Baues problem, namely that of a projection ?: P?Q where Q has only regular subdivisions andP has two more vertices than its dimension.