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Star operations on numerical semigroups: antichains and explicit results. (English) Zbl 1450.20020

Author’s abstract: The author introduced an order on the set of nondivisorial ideals of a numerical semigroup \(S\), and linked antichains of this order with the star operations on \(S\); subsequently, he used this order to find estimates on the number of star operations on \(S\). He then used them to find an asymptotic estimate on the number of nonsymmetric numerical semigroups with \(n\) or less star operations, and to determine these semigroups explicitly when \(n = 10\).

MSC:

20M14 Commutative semigroups
20M12 Ideal theory for semigroups
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References:

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