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
2019-01-01
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 $n=10$.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
