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arXiv · 2412.10884

Greedy Sets and Greedy Numerical Semigroups

Hebert Pérez-Rosés·José Miguel Serradilla-Merinero·Maria Bras-Amorós
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Abstract

Motivated by the change-making problem, we extend the notion of greediness to sets of positive integers not containing the element $1$, and from there to numerical semigroups. We provide an algorithm to determine if a given set (not necessarily containing the number $1$) 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.

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Hebert Pérez-Rosés, José Miguel Serradilla-Merinero, Maria Bras-Amorós. 2024-12-14. Greedy Sets and Greedy Numerical Semigroups. https://arxiv.org/abs/2412.10884

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