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

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 <TEX>${\gamma}$</TEX> of a coset diagram in a coset diagram is a polynomial f in <TEX>${\mathbb{Z}}$</TEX>[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.