Symmetric and Pseudo-Symmetric Numerical Semigroups via Young Diagrams and Their Semigroup Rings

2020/11/17 by Meral Süer, Süer, Meral, Mehmet Yeşi̇l +2 · 1 citation
Mathematics · #20M14 #20M20 #20M25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #math.AC #math.CO #math.GR #msc:20M14 #msc:20M20 #msc:20M25

paper · pdf · doi:10.48550/arxiv.2011.08540

arxiv created 2020/11/17 · openalex publication_date 2020/11/17 · arxiv updated 2020/11/18 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28

Abstract

This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric semigroups into an over semigroup and its dual. It is also given exactly for what kind of numerical semigroup S, the semigroup ring \Bbbk[ [S] ] has at least one Gorenstein subring and has at least one Kunz subring.

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• Young Diagram Decompositions for Almost Symmetric Numerical Semigroups

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