Greedy Sets and Greedy Numerical Semigroups
Combinatorics
2024-12-17 v1 Discrete Mathematics
Number Theory
Abstract
Motivated by the change-making problem, we extend the notion of greediness to sets of positive integers not containing the element , and from there to numerical semigroups. We provide an algorithm to determine if a given set (not necessarily containing the number ) is greedy. We also give specific conditions for sets of cardinality three, and we prove that numerical semigroups generated by three consecutive integers are greedy.
Cite
@article{arxiv.2412.10884,
title = {Greedy Sets and Greedy Numerical Semigroups},
author = {Hebert Pérez-Rosés and José Miguel Serradilla-Merinero and Maria Bras-Amorós},
journal= {arXiv preprint arXiv:2412.10884},
year = {2024}
}
Comments
Accepted for publication in Communications in Algebra, Taylor and Francis group. Contains 23 pages, 2 tables, 4 algorithms