Kunz languages for numerical semigroups are context sensitive
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908891640496128 |
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| author | Delgado, Manuel Cubertorer, Jaume Usó i |
| author_facet | Delgado, Manuel Cubertorer, Jaume Usó i |
| contents | There is a one-to-one and onto correspondence between the class of numerical semigroups of depth $n$, where $n$ is an integer, and a certain language over the alphabet $\{1,\ldots,n\}$ which we call a Kunz language of depth $n$. The Kunz language associated with the numerical semigroups of depth $2$ is the regular language $\{1,2\}^*2\{1,2\}^*$. We prove that Kunz languages associated with numerical semigroups of larger depth are context-sensitive but not regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03308 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kunz languages for numerical semigroups are context sensitive Delgado, Manuel Cubertorer, Jaume Usó i Formal Languages and Automata Theory Commutative Algebra 20M14, 68Q45 There is a one-to-one and onto correspondence between the class of numerical semigroups of depth $n$, where $n$ is an integer, and a certain language over the alphabet $\{1,\ldots,n\}$ which we call a Kunz language of depth $n$. The Kunz language associated with the numerical semigroups of depth $2$ is the regular language $\{1,2\}^*2\{1,2\}^*$. We prove that Kunz languages associated with numerical semigroups of larger depth are context-sensitive but not regular. |
| title | Kunz languages for numerical semigroups are context sensitive |
| topic | Formal Languages and Automata Theory Commutative Algebra 20M14, 68Q45 |
| url | https://arxiv.org/abs/2306.03308 |