IDEAS home Printed from https://ideas.repec.org/a/wly/jjmath/v2022y2022i1n4863429.html

Counting of Distinct Equivalence Classes of Circuits in PSL2, Z‐Space

Author

Listed:
  • Hanan Alolaiyan
  • Muhammad Aamir
  • Awais Yousaf
  • Abdul Razaq

Abstract

Graham Higman was the first who studied the transitive actions of the extended modular group PGL2, Z over PL(Fq) = Fq∪{∞} 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 x1x2π1x1x2−1π2x1x2π3,…,x1x2−1πl∈PSL2, Z, and it is denoted by (π1, π2, π3, …, πl). In this study, we shall formulate combinatorial sequences and find the number of distinct equivalence classes of a length‐6 circuit (π1, π2, π3, π4, π5, π6) for a fixed number of triangle Δ of class Π.

Suggested Citation

  • Hanan Alolaiyan & Muhammad Aamir & Awais Yousaf & Abdul Razaq, 2022. "Counting of Distinct Equivalence Classes of Circuits in PSL2, Z‐Space," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4863429
    DOI: 10.1155/2022/4863429
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/4863429
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/4863429?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hanan Alolaiyan & Abdul Razaq & Awais Yousaf & Rida Zahra & Kenan Yildirim, 2021. "A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, September.
    2. Muhammad Aamir & Muhammad Awais Yousaf & Abdul Razaq & Elena Guardo, 2021. "Number of Distinct Homomorphic Images in Coset Diagrams," Journal of Mathematics, Hindawi, vol. 2021, pages 1-39, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ahmed Badawy & Jesus A. Fisteus & Tarek M. Mahmoud & Tarek Abd El-Hafeez, 2021. "Topic Extraction and Interactive Knowledge Graphs for Learning Resources," Sustainability, MDPI, vol. 14(1), pages 1-21, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4863429. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/1469 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.