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.
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