Indian Journal of Science and Technology
Year: 2020, Volume: 13, Issue: 27, Pages: 2797-2810
Muhammad Nadeem Bari1*, Muhammad Aslam Malik1
1Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan
Email: [email protected]
Received Date:26 May 2020, Accepted Date:11 June 2020, Published Date:31 July 2020
Objectives: To determine the exact number of equivalence classes of G-circuits of length q≥2:Methods/Statistical Analysis: To classify G-orbits of Q(√m)/Q containing G-circuits of length 6. Findings: The equivalence classes of G-circuits of length 6 is ten in number and determine the exact number of G-orbits and structure of G-orbits corresponding to each of ten equivalence classes of Gcircuits. Furthermore, we describe some generalized G-circuits of length 2t corresponding to each of these ten equivalence classes and the structure of these G-circuits with conditions on t. Applications/Improvements: We employ Symmetries of Icosahedral group to explore cyclically equivalence classes of Gcircuits and similar G-circuits of length 6 corresponding to each of these ten equivalence classes. This study helps us in classifying reduced numbers lying in PSL(2, Z)-orbits. These results are verified by some suitable example.
Keywords: Rotational symmetries of icosahedral group; partition function;
equivalence classes of G-circuits; reduced quadratic irrational numbers
© 2020 Bari, Malik.This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee).
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