The number of circuits of length 4 in PSL(2, Z)-space

摘要

Professor Graham Higman has defined coset diagrams for the action of PGL(2,DOUBLE-STRUCK CAPITAL Z) on the projective line over a finite field F-q, denoted by PL(F-q), where q is a prime power. These diagrams are composed of circuits. In this paper, we answer the question, for a fixed number of triangles T, how many distinct circuits of length 4, are evolved?