Measurable sets with excluded distances
| dc.creator | Bukh, Boris | |
| dc.date | 2007-03-28 | |
| dc.date | 2008-02-24 | |
| dc.date.accessioned | 2026-07-07T09:22:40Z | |
| dc.date.available | 2026-07-07T09:22:40Z | |
| dc.description | For a set of distances D={d_1,...,d_k} a set A is called D-avoiding if no pair of points of A is at distance d_i for some i. We show that the density of A is exponentially small in k provided the ratios d_1/d_2, d_2/d_3, ..., d_{k-1}/d_k are all small enough. This resolves a question of Szekely, and generalizes a theorem of Furstenberg-Katznelson-Weiss, Falconer-Marstrand, and Bourgain. Several more results on D-avoiding sets are presented. | |
| dc.description | 23 pages, 3 figures, typos and small errors fixed | |
| dc.identifier | https://arxiv.org/abs/math/0703856 | |
| dc.identifier | http://arxiv.org/abs/math/0703856 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155458 | |
| dc.subject | Combinatorics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 52C10, 05D10 | |
| dc.title | Measurable sets with excluded distances | |
| dc.type | text |