On the number of collinear triples in permutations
| dc.creator | Li, Liangpan | |
| dc.date | 2008-02-05 | |
| dc.date | 2008-05-02 | |
| dc.date.accessioned | 2026-07-07T09:36:20Z | |
| dc.date.available | 2026-07-07T09:36:20Z | |
| dc.description | Let $α:\mathbb{Z}_n\to\mathbb{Z}_n$ be a permutation and $Ψ(α)$ be the number of collinear triples modulo $n$ in the graph of $α$. Cooper and Solymosi had given by induction the bound $\min_αΨ(α)\geq\lceil(n-1)/4\rceil$ when $n$ is a prime number. The main purpose of this paper is to give a direct proof of that bound. Besides, the expected number of collinear triples a permutation can have is also been determined. | |
| dc.description | 4 pages | |
| dc.identifier | https://arxiv.org/abs/0802.0572 | |
| dc.identifier | http://arxiv.org/abs/0802.0572 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160086 | |
| dc.subject | Combinatorics | |
| dc.subject | 51E15;11T99 | |
| dc.title | On the number of collinear triples in permutations | |
| dc.type | text |