A point-line incidence identity in finite fields, and applications

Brendan Murphy; Giorgis Petridis

A point-line incidence identity in finite fields, and applications

Combinatorics 2016-11-17 v3

Authors: Brendan Murphy , Giorgis Petridis

Abstract

Let $E \subseteq \mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the literature, not all naturally associated with lines in $\mathbb{F}_q^2$ , in a unified and elementary way.

Keywords

finite fields point-line incidence incidence function second moment combinatorial identity $\mathbb{F}_q^2$

Cite

@article{arxiv.1601.03981,
  title  = {A point-line incidence identity in finite fields, and applications},
  author = {Brendan Murphy and Giorgis Petridis},
  journal= {arXiv preprint arXiv:1601.03981},
  year   = {2016}
}

Comments

30 pages

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