2024/10/29 by Rajko Nenadov, Nenadov, Rajko
Mathematics · #Limits and Structures in Graph Theory #Advanced Topology and Set Theory #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.2410.21818
A subset of \mathbbFq2 is called an arc if it does not contain three collinear points. We show that there are at most \binom(1 + o(1))qm arcs of size m ≫ q1/2 (log q)3/2, nearly matching a trivial lower bound \binomqm. This was previously known to hold for m ≫ q2/3 (log q)3, due to Bhowmick and Roche-Newton. The lower bound on m is best possible up to a logarithmic factor.