Research Article

Numerical semigroups of coated odd elements

Published in: Quaestiones Mathematicae
Volume 49 , issue 1 , 2026 , pages: 53–69

DOI: 10.2989/16073606.2025.2550683

Author(s): M.B. Branco Universidade de Évora, , J.C. Rosales Universidad de Granada, Spain , M.A. Traesel Instituto Federal de São Paulo, Brazil

Keywords: Primary: 20M14 , Secondary: 11D07 , Frobenius number , gender , numerical semigroups , Frobenius family , Coe-semigroups and tree (associated to a Coe-semigroup)

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Abstract

A numerical semigroup S is coated with odd elements (Coe-semigroup), if {x − 1, x + 1} ⊆ S for all odd elements x in S. In this note, we will study this kind of numerical semigroup. In particular, we are interested in the study of the Frobenius number, gender and embedding dimension of a numerical semigroup of this type.

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