Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908791524556800 |
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| author | Stamate, Dumitru I. Strazzanti, Francesco |
| author_facet | Stamate, Dumitru I. Strazzanti, Francesco |
| contents | Given the integers $0<r_1<\dots<r_k$, we consider the shifted family of semigroups $M_n=\langle n, n+r_1,\dots, n+r_k\rangle$, where $n>0$. For sufficiently large $n$, we prove that if $M_n$ is nearly Gorenstein or almost symmetric, then so is $M_{n+r_k}$. A key ingredient is to relate the pseudo-Frobenius elements of $M_n$ and $M_{n+r_k}$, correcting a wrong claim in the literature. Moreover, we derive explicit formulas for the Frobenius and pseudo-Frobenius numbers of $M_{n+r_k}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19629 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups Stamate, Dumitru I. Strazzanti, Francesco Commutative Algebra 20M25, 20M14, 13H10 Given the integers $0<r_1<\dots<r_k$, we consider the shifted family of semigroups $M_n=\langle n, n+r_1,\dots, n+r_k\rangle$, where $n>0$. For sufficiently large $n$, we prove that if $M_n$ is nearly Gorenstein or almost symmetric, then so is $M_{n+r_k}$. A key ingredient is to relate the pseudo-Frobenius elements of $M_n$ and $M_{n+r_k}$, correcting a wrong claim in the literature. Moreover, we derive explicit formulas for the Frobenius and pseudo-Frobenius numbers of $M_{n+r_k}$. |
| title | Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups |
| topic | Commutative Algebra 20M25, 20M14, 13H10 |
| url | https://arxiv.org/abs/2601.19629 |