The study identifies the trivial automorphism group of power semigroups in numerical semigroups, indicating foundational properties in the structure of these mathematical objects.
If is a numerical semigroup (i.e., a cofinite subset of the non‐negative integers closed under addition), then the collection of all non‐empty subsets of forms 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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Tringali et al. (2026) studied this question.
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