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A problem of integer partitions and numerical semigroups

Published online by Cambridge University Press:  27 December 2018

J. C. Rosales
Affiliation:
Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain ([email protected])
M. B. Branco
Affiliation:
Departamento de Matem1ática, Universidade de Évora, 7000 Évora, Portugal ([email protected])

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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