• Connecting specific maps having two equal-sized faces and its genus

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0066

• # Keywords

Coset diagrams; januarials; triangle groups; Hecke groups and genus.

• # Abstract

Graham Higman introduced the concept of januarial as a specific map having two equal sized faces under the action of $\langle x, y : x^2 = y^k = (xy)^l = 1\rangle$ on a finite set. In this paper we take up the question posed by Graham Higman that what is the maximum number of circuits in the subgraph of a simple januarial for any value of $k$? We describe conditions under which januarials are connected and larger januarials are obtained. In an effort to look at topological features of the connected januarial, we find out genus of the januarial, genera of the two faces and number of circuits.

• # Author Affiliations

1. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019