On sets related to integer partitions with quasi-required elements and disallowed elements
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916189910859776 |
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| author | Robles-Pérez, Aureliano M. Rosales, José Carlos |
| author_facet | Robles-Pérez, Aureliano M. Rosales, José Carlos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10376 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On sets related to integer partitions with quasi-required elements and disallowed elements Robles-Pérez, Aureliano M. Rosales, José Carlos Number Theory Combinatorics 05A17, 11P81, 20M14 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. |
| title | On sets related to integer partitions with quasi-required elements and disallowed elements |
| topic | Number Theory Combinatorics 05A17, 11P81, 20M14 |
| url | https://arxiv.org/abs/2203.10376 |