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Graham Higman was the first who studied the transitive actions of the extended modular group  PGL 2 ,   Z over  PL F q = F q ∪ ∞ graphically and named it as coset diagram. In these sorts of graphs, a closed path of edges and triangles is known as a circuit. Coset diagrams evolve through the joining of these circuits. In a coset diagram, a circuit is termed as a length- l circuit if its one vertex is fixed by  x 1 x 2 π 1 x 1 x 2 − 1 π 2 x 1 x 2 π 3 , … , x 1 x 2 − 1 π l ∈ PSL 2 ,   Z , and it is denoted by  π 1 , π 2 , π 3 , … , π l . In this study, we shall formulate combinatorial sequences and find the number of distinct equivalence classes of a length-6 circuit  π 1 , π 2 , π 3 , π 4 , π 5 , π 6 for a fixed number of triangle  Δ of class  Π .

journal of mathematics

Counting of Distinct Equivalence Classes of Circuits in<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><mtext>PSL</mtext><mfenced open="(" close=")" separators="|"><mrow><mn>2</mn><mo>,</mo><mtext> </mtext><mi mathvariant="double-struck">Z</mi></mrow></mfenced></math>-Space

Counting of Distinct Equivalence Classes of Circuits inPSL2, Z-Space

Counting of Distinct Equivalence Classes of Circuits in $PSL (2, Z)$ -Space