Kunz languages for numerical semigroups are context sensitive

Delgado, Manuel; Usó i Cubertorer, Jaume

doi:10.2140/involve.2026.19.233

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Kunz languages for numerical semigroups are context sensitive

Manuel Delgado and Jaume Usó i Cubertorer

Vol. 19 (2026), No. 2, 233–248

DOI: 10.2140/involve.2026.19.233

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 ${1, \dots, n}$ , 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.

Keywords

numerical semigroup, Kunz languages, Chomsky hierarchy

Mathematical Subject Classification

Primary: 20M14, 68Q45

Milestones

Received: 23 July 2023

Revised: 5 September 2024

Accepted: 9 September 2024

Published: 8 March 2026

Communicated by Nathan Kaplan

Authors

Manuel Delgado
Departamento de Matemática Faculdade de Ciências CMUP–Centro de Matemática da Universidade do Porto Porto Portugal

Jaume Usó i Cubertorer
Departamento de Matemática Faculdade de Ciências CMUP–Centro de Matemática da Universidade do Porto Porto Portugal

Vol. 19, No. 2, 2026