On the number of collinear triples in permutations

Details On the number of collinear triples in permutations On the number of collinear triples in permutations

2008-02-05

arxiv.org/abs/0802.0572v2

Mathematics

Combinatorics

4 pages

Scientific paper

Let $\alpha:\mathbb{Z}_n\to\mathbb{Z}_n$ be a permutation and $\Psi(\alpha)$ be the number of collinear triples modulo $n$ in the graph of $\alpha$. Cooper and Solymosi had given by induction the bound $\min_{\alpha}\Psi(\alpha)\geq\lceil(n-1)/4\rceil$ 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.

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