Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of collinear triples in permutations   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.

24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph