Almost symmetric numerical semigroups with high type

We establish a one-to-one correspondence between numerical semigroups of genus g and almost symmetric numerical semigroups with Frobenius number F and type F − 2g , provided that F is greater than or equal to 4g − 1.The first author was partially supported by the Junta de Andalucía research group FQM-366, and by the project MTM2017-84890-P (MINECO/FEDER, UE). The second author was partially supported by the research groups FQM-024 (Junta de Extremadura/FEDER funds) and by the project MTM2015-65764-C3-1-P (MINECO/FEDER, UE) and by the project MTM2017-84890-P (MINECO/FEDER, UE)