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

      S MEHWISH Q MUSHTAQ

      Article Volume 130 Published: 18 November 2020 Article ID 0066

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      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

       

      S MEHWISH1 Q MUSHTAQ1

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

    • Dates

       
      Published
      18 November 2020
      Final version published online
      18 November 2020

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      Posted on July 25, 2019

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