Enumerating Regular Objects associated with Suzuki Groups

TL;DR

This paper employs the M"obius function of Suzuki groups to systematically count regular combinatorial objects like maps, hypermaps, and surface coverings that have automorphism groups isomorphic to Sz(q).

Contribution

It introduces a novel enumeration method using the M"obius function specific to Suzuki groups for counting regular objects.

Findings

Successful enumeration of regular objects with Sz(q) automorphism groups

Development of a new combinatorial enumeration technique

Enhanced understanding of symmetries in surface coverings

Abstract

We use the M\"obius function of the simple Suzuki group Sz(q) to enumerate regular objects such as maps, hypermaps, dessins d'enfants and surface coverings with automorphism groups isomorphic to Sz(q).