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A problem of integer partitions and numerical semigroups

Part of: Additive number theory; partitions Combinatorics Semigroups

Published online by Cambridge University Press:  27 December 2018

J. C. Rosales  and
M. B. Branco
J. C. Rosales
Affiliation:
Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain (jrosales@ugr.es)
M. B. Branco
Affiliation:
Departamento de Matem1ática, Universidade de Évora, 7000 Évora, Portugal (mbb@uevora.pt)
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Abstract

Let C be a set of positive integers. In this paper, we obtain an algorithm for computing all subsets A of positive integers which are minimals with the condition that if x1 + … + xn is a partition of an element in C, then at least a summand of this partition belongs to A. We use techniques of numerical semigroups to solve this problem because it is equivalent to give an algorithm that allows us to compute all the numerical semigroups which are maximals with the condition that has an empty intersection with the set C.

Keywords

integer partitionsnumerical semigroupsirreducibles numerical semigroupsApéry set

MSC classification

Primary: 05A17: Partitions of integers
Secondary: 11P81: Elementary theory of partitions 20M14: Commutative semigroups
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 4 , August 2019 , pp. 969 - 978
Copyright
Copyright © Royal Society of Edinburgh 2018 

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