The automorphism group of the power semigroup P(H) of any numerical semigroup H is trivial.
Tringali,Power monoids and their arithmetic: a survey, preprint (https://arxiv.org/abs/2602.15754)
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On the automorphisms of the power semigroups of a numerical semigroup
The automorphism group of the power semigroup P(H) of any numerical semigroup H is trivial.