A problem of Erdős about rich distances
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911945312960512 |
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| author | Bhowmick, Krishnendu |
| author_facet | Bhowmick, Krishnendu |
| contents | An old question posed by Erdős asked whether there exists a set of $n$ points such that $c \cdot n$ distances occur more than $n$ times. We provide an affirmative answer to this question, showing that there exists a set of $n$ points such that $\lfloor \frac{n}{4}\rfloor$ distances occur more than $n$ times. We also present a generalized version, finding a set of $n$ points where $c_m \cdot n$ distances occurring more than $n+m$ times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A problem of Erdős about rich distances Bhowmick, Krishnendu Combinatorics 52C10 An old question posed by Erdős asked whether there exists a set of $n$ points such that $c \cdot n$ distances occur more than $n$ times. We provide an affirmative answer to this question, showing that there exists a set of $n$ points such that $\lfloor \frac{n}{4}\rfloor$ distances occur more than $n$ times. We also present a generalized version, finding a set of $n$ points where $c_m \cdot n$ distances occurring more than $n+m$ times. |
| title | A problem of Erdős about rich distances |
| topic | Combinatorics 52C10 |
| url | https://arxiv.org/abs/2407.01174 |