Greedy Sets and Greedy Numerical Semigroups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Pérez-Rosés, Hebert Serradilla-Merinero, José Miguel Bras-Amorós, Maria |
| author_facet | Pérez-Rosés, Hebert Serradilla-Merinero, José Miguel Bras-Amorós, Maria |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Greedy Sets and Greedy Numerical Semigroups Pérez-Rosés, Hebert Serradilla-Merinero, José Miguel Bras-Amorós, Maria Combinatorics Discrete Mathematics Number Theory 06F05, 11Y55, 68R05 F.2.2; G.2.1 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. |
| title | Greedy Sets and Greedy Numerical Semigroups |
| topic | Combinatorics Discrete Mathematics Number Theory 06F05, 11Y55, 68R05 F.2.2; G.2.1 |
| url | https://arxiv.org/abs/2412.10884 |