On some classes of generalized numerical semigroups - Cisto Carmelo; Navarra Francesco (Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica)
A generalized numerical semigroup is a submonoid of ℕd 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 ⊆ℕd such that elements of ℕd \ S belong to the coordinate axes.