Carmelo Cisto, Rosanna Utano: On a family of numerical semigroups, 449-466

Abstract:

In this paper we introduce a family of numerical semigroups whose elements, given nonnegative integers $a,r,q,j_1$ satisfying certain conditions, are denoted by $\operatorname{L}(a,r,q,j_1)$. For such a class of numerical semigroups we compute its main invariants and verify Wilf's conjecture. If $L$ is a semigroup of the family, $\mathcal{A}$ is a numerical semigroup transform introduced in a previous paper by the first author, we study the numerical semigroup $\mathcal{A}(L)$ and provide a subfamily for which $\mathcal{A}$ produces a decreasing of the embedding dimension.

Key Words: Numerical semigroup, transforms, Wilf's conjecture, embedding dimension.

2020 Mathematics Subject Classification: Primary 20M14; Secondary 05C25, 11D07.

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