On sets related to integer partitions with quasi-required elements and disallowed elements
Metadatos
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Springer Nature
Materia
Integer partition Numerical semigroup Irreducible numerical semigroup Apéry set
Date
2023-10-13Referencia bibliográfica
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]
Patrocinador
Funding for open access publishing: Universidad de Granada/CBUA; “Proyecto de Excelencia de la Junta de Andalucía Grant Number ProyExcel 00868”; “Junta de Andalucía Grant Number FQM-343”; Funding for open access charge: Universidad de Granada/CBUARésumé
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.