The density of planar sets avoiding unit distances
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 is less than 1/4. Our argument implies the upper bound of 0.2470.
Elmentve itt :
| Szerzők: | |
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2024
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| Sorozat: | MATHEMATICAL PROGRAMMING
207 No. 1-2 |
| Tárgyszavak: | |
| doi: | 10.1007/s10107-023-02012-9 |
| mtmt: | 33834838 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/29680 |
| Tartalmi kivonat: | 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 is less than 1/4. Our argument implies the upper bound of 0.2470. |
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| Terjedelem/Fizikai jellemzők: | 303-327 |
| ISSN: | 0025-5610 |