Numerical semigroups of coated odd elements

Abstract

A numerical semigroup S is coated with odd elements (Coe-semigroup), if \x-1, x+1\⊂eq S for all odd element x in S. In this note, we will study this kind of numerical semigroups. 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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