Year: 2022
Type: preprint
Abstract: If a map has k transitivity classes of vertices that are subject to the action of the automorphism group, it is said to be k-uniform. The classification of 1-uniform maps on the torus is known. In this article, we classify 2-uniform maps on the torus up to isomorphism. Explicit formulas for the number of combinatorial types of these maps on number of vertices is obtained in terms of arithmetic functions in number theory, such as the divisor function. The asymptotic behaviour of these functions as number of vertices tends to infinity is also discussed and we obtained continuous functions which asymptotically served as upper and lower bounds.
Source: arXiv (Cornell University)
Authors: Kundu, Arnab, Maity, Dipendu
Institution: Indian Institute of Information Technology Guwahati
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4283367249