We introduce an order on the set of non-divisorial ideals of a numerical semigroup $S$, and link antichains of this order with the star operations on $S$; subsequently, we use this order to find estimates on the number of star operations on $S$. We then use 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 $n=10$.

Spirito, D. (2019). Star operations on numerical semigroups: antichains and explicit results. JOURNAL OF COMMUTATIVE ALGEBRA, 11(3), 401-431 [10.1216/JCA-2019-11-3-401].

Star operations on numerical semigroups: antichains and explicit results

Dario Spirito
2019

Abstract

We introduce an order on the set of non-divisorial ideals of a numerical semigroup $S$, and link antichains of this order with the star operations on $S$; subsequently, we use this order to find estimates on the number of star operations on $S$. We then use 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 $n=10$.
Spirito, D. (2019). Star operations on numerical semigroups: antichains and explicit results. JOURNAL OF COMMUTATIVE ALGEBRA, 11(3), 401-431 [10.1216/JCA-2019-11-3-401].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/325325
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