On the automorphisms of the power semigroups of a numerical semigroup
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917447796260864 |
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| author | Tringali, Salvatore Wen, Kerou |
| author_facet | Tringali, Salvatore Wen, Kerou |
| contents | If $H$ is a numerical semigroup (that is, a cofinite subset of the non-negative integers closed under addition), then the non-empty subsets of $H$ form a semigroup $\mathcal P(H)$ under the sumset operation induced by addition in $H$. Moreover, if $0 \in H$, then $\mathcal P(H)$ is a monoid with identity element $\{0\}$, and the family $\mathcal P_0(H)$ of all subsets of $H$ containing $0$ is a submonoid of $\mathcal P(H)$.
We show that the automorphism group of $\mathcal P(H)$ is trivial, and the same holds for $\mathcal P_0(H)$ when $0 \in H$. The proofs blend ideas from combinatorics and semigroup theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26901 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the automorphisms of the power semigroups of a numerical semigroup Tringali, Salvatore Wen, Kerou Number Theory Combinatorics Rings and Algebras If $H$ is a numerical semigroup (that is, a cofinite subset of the non-negative integers closed under addition), then the non-empty subsets of $H$ form a semigroup $\mathcal P(H)$ under the sumset operation induced by addition in $H$. Moreover, if $0 \in H$, then $\mathcal P(H)$ is a monoid with identity element $\{0\}$, and the family $\mathcal P_0(H)$ of all subsets of $H$ containing $0$ is a submonoid of $\mathcal P(H)$. We show that the automorphism group of $\mathcal P(H)$ is trivial, and the same holds for $\mathcal P_0(H)$ when $0 \in H$. The proofs blend ideas from combinatorics and semigroup theory. |
| title | On the automorphisms of the power semigroups of a numerical semigroup |
| topic | Number Theory Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2604.26901 |