| Autor: |
Gabriel Nivasch, János Pach, Rom Pinchasi, Shira Zerbib |
| Jazyk: |
angličtina |
| Rok vydání: |
2013 |
| Předmět: |
|
| Zdroj: |
Journal of Computational Geometry, Vol 4, Iss 1 (2013) |
| Druh dokumentu: |
article |
| ISSN: |
1920-180X |
| DOI: |
10.20382/jocg.v4i1a1 |
| Popis: |
Erdős conjectured in 1946 that every $n$-point set $P$ in convex position in the plane contains a point that determines at least $\lfloor n/2\rfloor$ distinct distances to the other points of $P$. The best known lower bound due to Dumitrescu (2006) is $13n/36 − O(1)$. In the present note, we slightly improve on this result to $(13/36 + \varepsilon)n − O(1)$ for $\varepsilon \approx 1/23000$. Our main ingredient is an improved bound on the maximum number of isosceles triangles determined by $P$. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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