On sets related to integer partitions with quasi-required elements and disallowed elements Robles Pérez, Aureliano M. Rosales González, José Carlos Integer partition Numerical semigroup Irreducible numerical semigroup Apéry set Given a set A of non-negative integers and a set B of positive integers, we are interested in computing all sets C (of positive integers) that are minimal in the family of sets K (of positive integers) such that (i) K contains no elements generated by non-negative integer linear combinations of elements in A and (ii) for any partition of an element in B there is at least one summand that belongs to K. To solve this question, we translate it into a numerical semigroups problem. 2023-10-31T10:39:00Z 2023-10-31T10:39:00Z 2023-10-13 info:eu-repo/semantics/article Robles-Pérez, A.M., Rosales, J.C. On sets related to integer partitions with quasi-required elements and disallowed elements. Aequat. Math. (2023). [https://doi.org/10.1007/s00010-023-01005-5] https://hdl.handle.net/10481/85366 10.1007/s00010-023-01005-5 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional Springer Nature