Cayley hyper-digraphs and Cayley hypermaps

TL;DR

This paper explores Cayley hyper-digraphs and hypermaps, focusing on their high symmetry properties and developing a general theory to facilitate their study.

Contribution

It introduces the concept of Cayley hyper-digraphs and hypermaps, and constructs highly symmetric examples, providing a foundational framework for future research.

Findings

Construction of Cayley hypermaps with high symmetry

Development of a general theory for Cayley hypermaps

Identification of automorphism groups with regular actions

Abstract

A Cayley hyper-digraph is a directed hypergraph that its automorphism group contains a subgroup acting regularly on vertices and a Cayley hypermap is a hypermap whose automorphism group contains a subgroup which induces regular action on the hypervertex set. In this paper, we study Cayley hyper-digraphs and construct Cayley hypermaps which have high level of symmetry. Our main goal is to present the general theory so as to make it clear to study Cayley hypermaps.