Robust additive bases without minimal subbases
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914280985591808 |
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| author | Larsen, Daniel Larsen, Michael |
| author_facet | Larsen, Daniel Larsen, Michael |
| contents | There exists a set $A$ of positive integers such that the number of representations of a large positive integer $m$ as a sum of two elements of $A$ grows with a lower bound of order $\log m$, but for which there is no subset $D$ of $A$ minimal for the property that $D+D$ contains all sufficiently large positive integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust additive bases without minimal subbases Larsen, Daniel Larsen, Michael Number Theory 11B13 (Primary) There exists a set $A$ of positive integers such that the number of representations of a large positive integer $m$ as a sum of two elements of $A$ grows with a lower bound of order $\log m$, but for which there is no subset $D$ of $A$ minimal for the property that $D+D$ contains all sufficiently large positive integers. |
| title | Robust additive bases without minimal subbases |
| topic | Number Theory 11B13 (Primary) |
| url | https://arxiv.org/abs/2601.18507 |