On some classes of generalized numerical semigroups

A generalized numerical semigroup is a submonoid of & Nopf;(d) with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups defined starting from numerical semigroups. In particular, we prove that the class of the so called T -stripe generalized numerical semigroups satisfies a generalization of Wilf's conjecture. Some partial results for the generalized Wilf's conjecture, together with characterizations for the properties of quasi-irreducibility and quasi-symmetry, are obtained for the so called T - graded semigroups and for the generalized numerical semigroups S subset of & Nopf;(d) such that elements of & Nopf;(d) \ S belong to the coordinate axes.