• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1367-1383
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• 2021

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 a numerical semigroup and its dual. It is also given exactly for what kind of numerical semigroup S, the semigroup ring 𝕜⟦S⟧ has at least one Gorenstein subring and has at least one Kunz subring.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.455-460
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• 2004

Let $S_{i}$ be the numerical semigroup generated by the set ${a,\;a{\;}+{\;}d,{\cdots},\;a+(i{\;}-{\;}l)d,\;a+(i{\;}+{\;}l)d,{\cdots},{\;}a{\;}+{\;}rd}$. In this paper, we will formulate the number of nonmembers of each set $S_{i}$ and find the if and only if conditions under which $S_1$ and $S_{r-1}$ are symmetric.