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Given a set A of non-negative integers and a set B of positive integers,weare interested in computing all sets C (of positive integers) that are minimalin the family of sets K (of positive integers) such that (i) K contains noelements generated by non-negative integer linear combinations of elements in Aand (ii) for any partition of an element in B there is at least one summandthat belongs to K. To solve this question, we translate it into a numericalsemigroups problem.

On sets related to integer partitions with quasi-required elements and disallowed elements