Enumeration of 4-regular one-face maps
Evgeniy Krasko, Alexander Omelchenko

TL;DR
This paper provides explicit formulas for counting 4-regular maps with a single face, both labeled and unlabeled, contributing to combinatorial map enumeration.
Contribution
It introduces explicit enumeration formulas for 4-regular one-face maps, advancing combinatorial map counting methods.
Findings
Derived formulas for labeled maps
Derived formulas for unlabeled maps
Enhanced understanding of 4-regular map enumeration
Abstract
We give explicit formulas enumerating 4-regular labelled and unlabelled one-face maps.
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