Kunz languages for numerical semigroups are context sensitive

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, , 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. (c) 2026 MSP (Mathematical Sciences Publishers).