Occurrence of right angles in vector spaces over finite fields

DOI10.1016/J.EJC.2017.12.005zbMATH Open1388.51004arXiv1511.08942OpenAlexW2794356993MaRDI QIDQ1746574

Michael Bennett

Publication date: 25 April 2018

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Abstract: Here we examine some Erdos-Falconer-type problems in vector spaces over finite fields involving right angles. Our main goals are to show that a) a subset A of F_q^d of size >> q^[(d+2)/3] contains three points which generate a right angle, and b) a subset A of F_q^d of size >> q^[(d+2)/2] contains two points which generate a right angle with the vertex at the origin. We will also prove that b) is sharp up to constants and provide some partial results for similar problems related to spread and collinear triples.

Full work available at URL: https://arxiv.org/abs/1511.08942

zbMATH Keywords

vector spaces over finite fieldsErdős-Falconer-type problemsright angles

Mathematics Subject Classification ID

Combinatorial geometries and geometric closure systems (51D20)

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Related Items (3)

The partition rank of a tensor and \(k\)-right corners in \(\mathbb{F}_q^n\) ⋮ Avoiding right angles and certain Hamming distances ⋮ Maximum subsets of \(\mathbb{F}^n_q\) containing no right angles

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