Joining of circuits in $PSL(2,\mathbb{Z})$-space

Qaiser Mushtaq; Abdul Razaq

doi:10.4134/BKMS.2015.52.6.2047

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(6): 2047-2069

Printed November 30, 2015

https://doi.org/10.4134/BKMS.2015.52.6.2047

Joining of circuits in $PSL(2,\mathbb{Z})$-space

Qaiser Mushtaq and Abdul Razaq

Quaid-i-Azam University Islamabad, Quaid-i-Azam University Islamabad

Abstract

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Abstract

The coset diagrams are composed of fragments, and the fragments are further composed of circuits at a certain common point. A condition for the existence of a certain fragment $\gamma $ of a coset diagram in a coset diagram is a polynomial $f$ in $ \mathbb{Z} \lbrack z].$ In this paper, we answer the question: how many polynomials are obtained from the fragments, evolved by joining the circuits $\left( n,n\right) $ and $\left( m,m\right) ,$ where $n

Keywords: modular group, coset diagrams, projective line over finite field

MSC numbers: Primary 05C25; Secondary 20G40