On the Classification of Telescopic Numerical Semigroups of Some Fixed Multiplicity

Ying Wang, Muhammad Ahsan Binyamin (), Iqra Amin, Adnan Aslam () and Yongsheng Rao
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Ying Wang: Department of Network, Software Engineering Institute of Guangzhou, Guangzhou 510980, 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

Mathematics, 2022, vol. 10, issue 20, 1-9

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.

Keywords: telescopic numerical semigroup; embedding dimension; multiplicity; genus; Frobenius number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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