Almost all Cayley maps are mapical regular representations
Combinatorics
2023-01-20 v1 Group Theory
Abstract
Cayley maps are combinatorial structures built upon Cayley graphs on a group. As such the original group embeds in their group of automorphisms, and one can ask in which situation the two coincide (one then calls the Cayley map a mapical regular representation or MRR) and with what probability. The first question was answered by Jajcay. In this paper we tackle the probabilistic version, and prove that as groups get larger the proportion of MRRs among all Cayley Maps approaches 1.
Keywords
Cite
@article{arxiv.2301.08220,
title = {Almost all Cayley maps are mapical regular representations},
author = {Dario Sterzi and Pablo Spiga},
journal= {arXiv preprint arXiv:2301.08220},
year = {2023}
}
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7 pages