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JOINING OF CIRCUITS IN PSL(2, ℤ)-SPACE

  • MUSHTAQ, QAISER (Department of Mathematics Quaid-i-Azam University Islamabad) ;
  • RAZAQ, ABDUL (Department of Mathematics Quaid-i-Azam University Islamabad)
  • Received : 2014.11.04
  • Published : 2015.11.30

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 ${\mathbb{Z}}$[z]. In this paper, we answer the question: how many polynomials are obtained from the fragments, evolved by joining the circuits (n, n) and (m, m), where n < m, at all points.

Keywords

modular group;coset diagrams;projective line over finite field

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