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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.01835 |
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| _version_ | 1866911992494686208 |
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| author | Kravitz, Noah |
| author_facet | Kravitz, Noah |
| contents | A conjecture of Graham (repeated by Erdős) asserts that for any set $A \subseteq \mathbb{F}_p \setminus \{0\}$, there is an ordering $a_1, \ldots, a_{|A|}$ of the elements of $A$ such that the partial sums $a_1, a_1+a_2, \ldots, a_1+a_2+\cdots+a_{|A|}$ are all distinct. We give a very short proof of this conjecture for sets $A$ of size at most $\log p/\log\log p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rearranging small sets for distinct partial sums Kravitz, Noah Combinatorics A conjecture of Graham (repeated by Erdős) asserts that for any set $A \subseteq \mathbb{F}_p \setminus \{0\}$, there is an ordering $a_1, \ldots, a_{|A|}$ of the elements of $A$ such that the partial sums $a_1, a_1+a_2, \ldots, a_1+a_2+\cdots+a_{|A|}$ are all distinct. We give a very short proof of this conjecture for sets $A$ of size at most $\log p/\log\log p$. |
| title | Rearranging small sets for distinct partial sums |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.01835 |