We study the cardinality of the set Star(S) of star operations on a numerical semigroup S; in particular, we study ways to estimate Star(S) and to bound the number of nonsymmetric numerical semigroups such that |Star(S)|≤ n. We also study this problem in the setting of analytically irreducible, residually rational rings whose integral closure is a fixed discrete valuation ring.
The Number of Star Operations on Numerical Semigroups and on Related Integral Domains
Spirito D.
2020
Abstract
We study the cardinality of the set Star(S) of star operations on a numerical semigroup S; in particular, we study ways to estimate Star(S) and to bound the number of nonsymmetric numerical semigroups such that |Star(S)|≤ n. We also study this problem in the setting of analytically irreducible, residually rational rings whose integral closure is a fixed discrete valuation ring.
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