The genus, the Frobenius number, and the pseudo-Frobenius numbers of numerical semigroups of type two Robles-Pérez, Aureliano M. Rosales González, José Carlos Frobenius number Pseudo-Frobenius number Numerical semigroups Genus Type This article has been published in a revised form in "Proceedings of the Royal Society of Edinburgh. Section A: Mathematics" https://doi.org/10.1017S0308210515000840. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright Cambridge University Press. In this paper we study some questions on numerical semigroups of type two. On the one hand, we investigate the relation between the genus and the Frobenius number. On the other hand, for two fixed positive integers g1, g2, we give necessary and sufficient conditions in order to have a numerical semigroup S such that {g1, g2} is the set of its pseudo-Frobenius numbers and, moreover, we build explicitly families of such numerical semigroups. 2018-03-05T13:34:21Z 2018-03-05T13:34:21Z 2016-07-19 info:eu-repo/semantics/article Robles-Pérez, A.M.; Rosales González, J.C. The genus, the Frobenius number, and the pseudo-Frobenius numbers of numerical semigroups of type two. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, 146(5): 1081-1090 (2016). [http://hdl.handle.net/10481/49818] 0308-2105 1473-7124 http://hdl.handle.net/10481/49818 10.1017/S0308210515000840 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Cambridge University Press; Royal Society of Edinburgh