TL;DR
This paper investigates star operations on Kunz domains, a special class of domains linked to numerical semigroups, refutes a previous conjecture, and provides estimates and exact counts for star operations in specific cases.
Contribution
It introduces new insights into star operations on Kunz domains, refutes a conjecture, and offers enumeration results for star operations in certain scenarios.
Findings
Refutes a conjecture of Houston, Mimouni, and Park.
Provides an estimate for the number of star operations in a specific case.
Achieves exact counting of star operations in a sub-case.
Abstract
We study star operations on Kunz domains, a class of analytically irreducible, residually rational domains associated to pseudo-symmetric numerical semigroups, and we use them to refute a conjecture of Houston, Mimouni and Park. We also find an estimate for the number of star operations in a particular case, and a precise counting in a sub-case.
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