On sets related to integer partitions with quasi-required elements and disallowed elements
Preprint
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
All Related Versions
This publication has 5 references indexed in Scilit:
- Maximality Properties in Numerical Semigroups, with Applications to One-Dimensional Analytically Irreducible Local Domains2023
- A problem of integer partitions and numerical semigroupsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 2018
- On the enumeration of the set of numerical semigroups with fixed Frobenius numberComputers & Mathematics with Applications, 2012
- The tree of irreducible numerical semigroups with fixed Frobenius numberForum Mathematicum, 2011
- Irreducible numerical semigroupsPacific Journal of Mathematics, 2003