The density of planar sets avoiding unit distances
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914845468655616 |
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| author | Ambrus, Gergely Csiszárik, Adrián Matolcsi, Máté Varga, Dániel Zsámboki, Pál |
| author_facet | Ambrus, Gergely Csiszárik, Adrián Matolcsi, Máté Varga, Dániel Zsámboki, Pál |
| contents | By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances cannot exceed $1/4$. Our argument implies the upper bound of $0.2470$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14179 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The density of planar sets avoiding unit distances Ambrus, Gergely Csiszárik, Adrián Matolcsi, Máté Varga, Dániel Zsámboki, Pál Metric Geometry 42B05, 52C10, 52C17, 90C05 By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances cannot exceed $1/4$. Our argument implies the upper bound of $0.2470$. |
| title | The density of planar sets avoiding unit distances |
| topic | Metric Geometry 42B05, 52C10, 52C17, 90C05 |
| url | https://arxiv.org/abs/2207.14179 |