Cayley extensions of maniplexes and polytopes

IF 0.9 2区 数学 Q2 MATHEMATICS
Gabe Cunningham , Elías Mochán , Antonio Montero
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引用次数: 0

Abstract

A map on a surface whose automorphism group has a subgroup acting regularly on its vertices is called a Cayley map. Here we generalize that notion to maniplexes and polytopes. We define M to be a Cayley extension of K if the facets of M are isomorphic to K and if some subgroup of the automorphism group of M acts regularly on the facets of M. We show that many natural extensions in the literature on maniplexes and polytopes are in fact Cayley extensions. We also describe several universal Cayley extensions. Finally, we examine the automorphism group and symmetry type graph of Cayley extensions.
复形和多面体的Cayley扩展
曲面上的自同构群在其顶点上有规则作用的子群的映射称为Cayley映射。这里我们把这个概念推广到复形和多面体。如果M的面与K同构,并且M的自同构群的某子群规律地作用于M的面,我们定义M是K的Cayley扩展。我们证明了文献中许多关于复形和多面体的自然扩展实际上是Cayley扩展。我们还描述了几个通用的Cayley扩展。最后,我们研究了Cayley扩展的自同构群和对称型图。
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来源期刊
CiteScore
2.90
自引率
9.10%
发文量
94
审稿时长
12 months
期刊介绍: The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
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