On a family of numerical semigroups

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 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, A is a numerical semigroup transform introduced in a previous paper by the first author, we study the numerical semigroup A(L) and provide a subfamily for which A produces a decreasing of the embedding dimension.