English

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

Number Theory 2024-04-04 v2 Combinatorics

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

Cite

@article{arxiv.2203.10376,
  title  = {On sets related to integer partitions with quasi-required elements and disallowed elements},
  author = {Aureliano M. Robles-Pérez and José Carlos Rosales},
  journal= {arXiv preprint arXiv:2203.10376},
  year   = {2024}
}

Comments

17 pages; typos corrected

R2 v1 2026-06-24T10:19:15.861Z