On the automorphisms of the power semigroups of a numerical semigroup
Salvatore Tringali, Kerou Wen

TL;DR
This paper proves that the automorphism groups of the power semigroups of a numerical semigroup are trivial, using combinatorics and semigroup theory, revealing structural rigidity.
Contribution
It establishes the triviality of automorphism groups for power semigroups of numerical semigroups, a novel result in algebraic combinatorics.
Findings
Automorphism group of (H) is trivial.
Automorphism group of (H) with 0 in H is trivial.
Proofs combine combinatorics and semigroup theory.
Abstract
If is a numerical semigroup (that is, a cofinite subset of the non-negative integers closed under addition), then the non-empty subsets of form a semigroup under the sumset operation induced by addition in . Moreover, if , then is a monoid with identity element , and the family of all subsets of containing is a submonoid of . We show that the automorphism group of is trivial, and the same holds for when . The proofs blend ideas from combinatorics and semigroup theory.
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