Dense arrangements are locally very dense I
| dc.creator | Solymosi, Jozsef | |
| dc.date | 2005-04-01 | |
| dc.date.accessioned | 2026-07-07T05:18:42Z | |
| dc.date.available | 2026-07-07T05:18:42Z | |
| dc.description | The Szemerédi-Trotter theorem gives a bound on the maximum number of incidences between points and lines on the Euclidean plane. In particular it says that $n$ lines and $n$ points determine $O(n^{4/3})$ incidences. Let us suppose that an arrangement of $n$ lines and $n$ points defines $cn^{4/3}$ incidences, for a given positive $c.$ It is widely believed that such arrangements have special structure, but no results are known in this direction. Here we show that for any natural number, $k,$ one can find $k$ points of the arrangement in general position such that any pair of them is incident to a line from the arrangement, provided by $n\geq n_0(k).$ In a subsequent paper we will establish similar statement to hyperplanes. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504009 | |
| dc.identifier | http://arxiv.org/abs/math/0504009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74757 | |
| dc.subject | Combinatorics | |
| dc.subject | 52C10 | |
| dc.title | Dense arrangements are locally very dense I | |
| dc.type | text |