Symmetric generalized numerical semigroups in $\mathbb{N}^d$ with embedding dimension $2d+1$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912478023122944 |
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| author | Bhardwaj, Om Prakash Cisto, Carmelo |
| author_facet | Bhardwaj, Om Prakash Cisto, Carmelo |
| contents | In this article, we classify all symmetric generalized numerical semigroups in $\mathbb{N}^d$ of embedding dimension $2d+1$. Consequently, we show that in this case the property of being symmetric is equivalent to have a unique maximal gap with respect to natural partial order in $\mathbb{N}^d$. Moreover, we deduce that when $d>1$, there does not exist any generalized numerical semigroup of embedding dimension $2d+1$, which is almost symmetric but not symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric generalized numerical semigroups in $\mathbb{N}^d$ with embedding dimension $2d+1$ Bhardwaj, Om Prakash Cisto, Carmelo Commutative Algebra 20M14, 11D07 In this article, we classify all symmetric generalized numerical semigroups in $\mathbb{N}^d$ of embedding dimension $2d+1$. Consequently, we show that in this case the property of being symmetric is equivalent to have a unique maximal gap with respect to natural partial order in $\mathbb{N}^d$. Moreover, we deduce that when $d>1$, there does not exist any generalized numerical semigroup of embedding dimension $2d+1$, which is almost symmetric but not symmetric. |
| title | Symmetric generalized numerical semigroups in $\mathbb{N}^d$ with embedding dimension $2d+1$ |
| topic | Commutative Algebra 20M14, 11D07 |
| url | https://arxiv.org/abs/2505.11091 |