Products of abstract polytopes

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:157

Article

Gleason, Ian¹  Hubard, Isabel² 

[1] Univ Calif Berkeley, Berkeley, CA 94720 USA

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City, DF, Mexico

关键词: Abstract polytopes;    Join product;    Cartesian product;    Direct sum;    Monodromy groups;   

DOI  :  10.1016/j.jcta.2018.02.002

来源: Elsevier

【 摘 要 】

Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological product, which also arises in a natural way. We show that these products have unique prime factorization theorems. We use this to compute the automorphism group of a product in terms of the automorphism groups of the factors and show that (non trivial) products are almost never regular or two-orbit poly topes. We finish the paper by studying the monodromy group of a product, show that such a group is always an extension of a symmetric group, and give some examples in which this extension splits. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free