Enumeration of Regular Maps on Surfaces of a Given Genus
E.S. Krasko, A.V. Omelchenko

TL;DR
This paper develops methods to count rooted and unrooted d-regular maps on oriented surfaces of genus g, with special focus on maps with a single face, advancing combinatorial enumeration techniques.
Contribution
It provides new enumeration formulas for d-regular maps on surfaces of arbitrary genus, including detailed analysis of maps with a single face.
Findings
Derived enumeration formulas for rooted and unrooted d-regular maps.
Analyzed the special case of maps with a single face in detail.
Extended combinatorial enumeration to surfaces of arbitrary genus.
Abstract
In the present work the rooted and unrooted d-regular maps on 2-dimentional oriented surfaces of genus g are enumerated. Separately and in more detail the case of d-regular maps with a single face are considered.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Topics in Algebra · Coding theory and cryptography
