On the Enumeration of the Set of Numerical Semigroups with Fixed Frobenius Number and Fixed Number of Second Kind Gaps Robles Pérez, Aureliano M. Rosales González, José Carlos Irreducible numerical semigroups Second kind gaps Frobenius number Trees Wilf’s conjecture Both authors are supported by the Project MTM2017-84890-P (funded by Ministerio de Economía, Industria y Competitividad and Fondo Europeo de Desarrollo Regional FEDER) and by the Junta de Andalucía Grant Number FQM-343. The authors would like to thank the referee for useful comments and suggestions that have helped us to improve the manuscript. We study how certain invariants of numerical semigroups relate to the number of second kind gaps. Furthermore, given two fixed non-negative integers F and k, we provide an algorithm to compute all the numerical semigroups whose Frobenius number is F and which have exactly k second kind gaps. 2021-11-29T11:10:56Z 2021-11-29T11:10:56Z 2021-11-12 journal article Robles-Pérez, A.M., Rosales, J.C. On the Enumeration of the Set of Numerical Semigroups with Fixed Frobenius Number and Fixed Number of Second Kind Gaps. Results Math 77, 10 (2022). [https://doi.org/10.1007/s00025-021-01542-y] http://hdl.handle.net/10481/71813 10.1007/s00025-021-01542-y eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España Springer Nature