On sets related to integer partitions with quasi-required elements and disallowed elements
Open Access
- 13 October 2023
- journal article
- research article
- Published by Springer Nature in Aequationes mathematicae
- Vol. 98 (2) , 423-440
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 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.Keywords
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Funding Information
- Junta de Andalucía (FQM-343)
- Proyecto de Excelencia de la Junta de Andalucía (Grant Number ProyExcel 00868)
- Universidad de Granada
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