Collinear triples in permutations

2008/05/04 by Liangpan Li, Li, Liangpan
Computer Science · Engineering · Mathematics · #11T99 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:11T99

paper · pdf · doi:10.48550/arxiv.0805.0410

4 pages

arxiv created 2008/05/04 · openalex publication_date 2008/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let α:\mathbbF_q→\mathbbF_q be a permutation and Ψ(α) be the number of collinear triples in the graph of α, where \mathbbF_q denotes a finite field of q elements. When q is odd Cooper and Solymosi once proved Ψ(α)≥(q-1)/4 and conjectured the sharp bound should be Ψ(α)≥(q-1)/2. In this note we indicate that the Cooper-Solymosi conjecture is true.

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