A note on iterated sumsets races
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909612797591552 |
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| author | Péringuey, Paul de Roton, Anne |
| author_facet | Péringuey, Paul de Roton, Anne |
| contents | This short note answers a question raised by Nathanson \cite{Nath25} about "races" between iterated sumsets. We prove that for any integer $n$, there are finite sets of integers $A$ and $B$ with same diameter such that the signs of the elements of the sequence $(|hA|-|hB|)_h$ changes at least $n$ times. Kravitz proved in \cite{Kravitz} a much better result. This brief and modest note may serve as a stepping stone towards his work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on iterated sumsets races Péringuey, Paul de Roton, Anne Number Theory Combinatorics 11P70 This short note answers a question raised by Nathanson \cite{Nath25} about "races" between iterated sumsets. We prove that for any integer $n$, there are finite sets of integers $A$ and $B$ with same diameter such that the signs of the elements of the sequence $(|hA|-|hB|)_h$ changes at least $n$ times. Kravitz proved in \cite{Kravitz} a much better result. This brief and modest note may serve as a stepping stone towards his work. |
| title | A note on iterated sumsets races |
| topic | Number Theory Combinatorics 11P70 |
| url | https://arxiv.org/abs/2505.11233 |