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arXiv · 2306.03308

Kunz languages for numerical semigroups are context sensitive

Manuel Delgado·Jaume Usó i Cubertorer
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Abstract

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.

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Manuel Delgado, Jaume Usó i Cubertorer. 2023-06-05. Kunz languages for numerical semigroups are context sensitive. https://doi.org/10.2140/involve.2026.19.233

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