Collinear Triple Hypergraphs and the Finite Plane Kakeya Problem
| dc.creator | Cooper, Joshua N. | |
| dc.date | 2006-07-28 | |
| dc.date | 2006-08-14 | |
| dc.date.accessioned | 2026-07-07T07:21:06Z | |
| dc.date.available | 2026-07-07T07:21:06Z | |
| dc.description | We show that the problem of counting collinear points in a permutation (previously considered by the author and J. Solymosi in "Collinear Points in Permutations", 2005) and the well-known finite plane Kakeya problem are intimately connected. Via counting arguments and by studying the hypergraph of collinear triples we show a new lower bound (5q/14 + O(1)) for the number of collinear triples of a permutation of GF(q) and a new lower bound (q(q + 1)/2 + 5q/14 + O(1)) on the size of the smallest Besicovitch set in GF(q)^2. Several interesting questions about the structure of the collinear triple hypergraph are presented. | |
| dc.description | 17 pages, no figures. Typos fixed, arithmetic errors fixed. A big thanks to Xander Faber for his help | |
| dc.identifier | https://arxiv.org/abs/math/0607734 | |
| dc.identifier | http://arxiv.org/abs/math/0607734 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115184 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 51E15; 14N10 | |
| dc.title | Collinear Triple Hypergraphs and the Finite Plane Kakeya Problem | |
| dc.type | text |