Graham's rearrangement conjecture beyond the rectification barrier
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929664645136384 |
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| author | Bedert, Benjamin Kravitz, Noah |
| author_facet | Bedert, Benjamin Kravitz, Noah |
| contents | A 1971 conjecture of Graham (later repeated by Erdős and Graham) asserts that every set $A \subseteq \mathbb{F}_p \setminus \{0\}$ has an ordering whose partial sums are all distinct. We prove this conjecture for sets of size $|A| \leqslant e^{(\log p)^{1/4}}$; our result improves the previous bound of $\log p/\log \log p$. One ingredient in our argument is a structure theorem involving dissociated sets, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graham's rearrangement conjecture beyond the rectification barrier Bedert, Benjamin Kravitz, Noah Combinatorics Number Theory A 1971 conjecture of Graham (later repeated by Erdős and Graham) asserts that every set $A \subseteq \mathbb{F}_p \setminus \{0\}$ has an ordering whose partial sums are all distinct. We prove this conjecture for sets of size $|A| \leqslant e^{(\log p)^{1/4}}$; our result improves the previous bound of $\log p/\log \log p$. One ingredient in our argument is a structure theorem involving dissociated sets, which may be of independent interest. |
| title | Graham's rearrangement conjecture beyond the rectification barrier |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2409.07403 |