Departamento de Matemáticas, Estadística e I.O. Sección de Matemáticas, Universidad de La Laguna, Apartado de Correos 456, 38200 La Laguna, Spain
J. I. García-García
Department of Mathematics/INDESS (Instituto Universitario para el Desarrollo Social Sostenible), University of Cadiz, 11510 Puerto Real, Spain
A. Vigneron-Tenorio
Department of Mathematics/INDESS (Instituto Universitario para el Desarrollo Social Sostenible), University of Cadiz, 11406 Jerez de la Frontera, Spain
In this work, we present a new class of numerical semigroups called GSI-semigroups. We see the relations between them and other families of semigroups and we explicitly give their set of gaps. Moreover, an algorithm to obtain all the GSI-semigroups up to a given Frobenius number is provided and the realization of positive integers as Frobenius numbers of GSI-semigroups is studied.
