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

Authors:
  • ARAureliano M. Robles-Pérez
    Aureliano M. Robles-Pérez
  • JRJosé Carlos Rosales
    José Carlos Rosales
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Abstract
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 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.