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On the Classification of Telescopic Numerical Semigroups of Some Fixed Multiplicity

Author

Listed:
  • Ying Wang

    (Department of Network, Software Engineering Institute of Guangzhou, Guangzhou 510980, China
    Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Muhammad Ahsan Binyamin

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan)

  • Iqra Amin

    (Department of Mathematics, Government College University, Faisalabad 38000, Pakistan)

  • Adnan Aslam

    (Department of Natural Sciences and Humanities, University of Engineering and Technology, Lahore 54000, Pakistan)

  • Yongsheng Rao

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

Abstract

The telescopic numerical semigroups are a subclass of symmetric numerical semigroups widely used in algebraic geometric codes. Suer and Ilhan gave the classification of triply generated telescopic numerical semigroups up to multiplicity 10 and by using this classification they computed some important invariants in terms of the minimal system of generators. In this article, we extend the results of Suer and Ilhan for telescopic numerical semigroups of multiplicities 8 and 12 with embedding dimension four. Furthermore, we compute two important invariants namely the Frobenius number and genus for these classes in terms of the minimal system of generators.

Suggested Citation

  • Ying Wang & Muhammad Ahsan Binyamin & Iqra Amin & Adnan Aslam & Yongsheng Rao, 2022. "On the Classification of Telescopic Numerical Semigroups of Some Fixed Multiplicity," Mathematics, MDPI, vol. 10(20), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3871-:d:946432
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