Cookies?
Library Header Image
LSE Research Online LSE Library Services

Elementary incidence theorems for complex numbers and quaternions

Solymosi, József and Swanepoel, Konrad (2008) Elementary incidence theorems for complex numbers and quaternions. SIAM Journal on Discrete Mathematics, 22 (3). pp. 1145-1148. ISSN 0895-4801

Full text not available from this repository.

Abstract

We present some elementary ideas to prove the following Sylvester–Gallai type theorems involving incidences between points and lines in the planes over the complex numbers and quaternions. 1. Let $A$ and $B$ be finite sets of at least two complex numbers each. Then there exists a line $\ell$ in the complex affine plane such that $\lvert(A\times B)\cap\ell\rvert=2$. 2. Let $S$ be a finite noncollinear set of points in the complex affine plane. Then there exists a line $\ell$ such that $2\leq \lvert S\cap\ell\rvert \leq 5$. 3. Let $A$ and $B$ be finite sets of at least two quaternions each. Then there exists a line $\ell$ in the quaternionic affine plane such that $2\leq \lvert(A\times B)\cap\ell\rvert \leq 5$. 4. Let $S$ be a finite noncollinear set of points in the quaternionic affine plane. Then there exists a line $\ell$ such that $2\leq \lvert S\cap\ell\rvert \leq 24$.

Item Type: Article
Official URL: http://www.siam.org/journals/sidma.php
Additional Information: © 2009 SIAM
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Oct 2009 09:34
URL: http://eprints.lse.ac.uk/25420/

Actions (login required)

Record administration - authorised staff only Record administration - authorised staff only