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

Brendan Murphy; Giorgis Petridis

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

Brendan Murphy, Giorgis Petridis

Pure Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

13 Citations (Scopus)

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.

Original language	Undefined/Unknown
Journal	Moscow Journal of Combinatorics and Number Theory,
Publication status	Published - 15 Jan 2016

Bibliographical note

30 pages

Keywords

math.CO

Handle.net

Persistent link

Cite this

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AU - Petridis, Giorgis

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N2 - 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.

AB - 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.

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M3 - Article (Academic Journal)

JO - Moscow Journal of Combinatorics and Number Theory,

JF - Moscow Journal of Combinatorics and Number Theory,

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