Integral point sets over finite fields
| dc.creator | Kurz, Sascha | |
| dc.date | 2008-04-08 | |
| dc.date.accessioned | 2026-07-07T09:31:04Z | |
| dc.date.available | 2026-07-07T09:31:04Z | |
| dc.description | We consider point sets in the affine plane $\mathbb{F}_q^2$ where each Euclidean distance of two points is an element of $\mathbb{F}_q$. These sets are called integral point sets and were originally defined in $m$-dimensional Euclidean spaces $\mathbb{E}^m$. We determine their maximal cardinality $\mathcal{I}(\mathbb{F}_q,2)$. For arbitrary commutative rings $\mathcal{R}$ instead of $\mathbb{F}_q$ or for further restrictions as no three points on a line or no four points on a circle we give partial results. Additionally we study the geometric structure of the examples with maximum cardinality. | |
| dc.description | 22 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0804.1289 | |
| dc.identifier | http://arxiv.org/abs/0804.1289 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158332 | |
| dc.subject | Combinatorics | |
| dc.subject | 51E20 | |
| dc.title | Integral point sets over finite fields | |
| dc.type | text |