The Erdős-Ko-Rado theorem for vector spaces
type: Item
instance of: scholarly article
title: The Erdős-Ko-Rado theorem for vector spaces
zbMATH Open document ID: 0609.05055
DOI: 10.1016/0097-3165(86)90063-4
author: Peter Frankl
author: Richard M. Wilson
published in: Journal of Combinatorial Theory. Series A
publication date: 1986-01-01T00:00:00Z
review text: The classical Erdős-Ko-Rado problem was studied in many aspects: In 1975 W. N. Hsieh proved the first analogue theorem in finite vector spaces. In this case two subspaces are intersecting, if their common part in properly subspace. Let V be an n-dimensional vector space over GF(q) and for integers \(k\geq t>0\) let \(m_ q(n,k,t)\) denote the maximum possible number of subspaces in a t-intersecting family \({\mathcal F}\) of k- dimensional subspaces of V i.e. dim \(F\cap F'\geq t\) holds for all F,F'\(\in {\mathcal F}\). Hshieh proved in 1975 that \(m_ q(n,k,t)=\left[ \begin{matrix} n-t\\ k-t\end{matrix} \right]\) holds for \(n\geq 2k+1\), \(q\geq 3\) and for \(n\geq 2k+2\), \(q=2.\) In the paper under review it is proved: Theorem 1: Suppose \(n\geq 2k-t\); \({\mathcal F}\subset \left[ \begin{matrix} V\\ k\end{matrix} \right]\) is t- intersecting then \[ | {\mathcal F}| \leq \max \{\left[ \begin{matrix} n-t\\ k-t\end{matrix} \right]_ q;\quad \left[ \begin{matrix} 2k-t\\ k\end{matrix} \right]_ q\}. \] The proof method is based on the ideas of the second author.
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 3985272
zbMATH Keywords: Erdős-Ko-Rado theorem
zbMATH Keywords: finite vector spaces over GF(q)
zbMATH Keywords: Hsieh's theorem
Wikidata QID: Q56213502
reviewed by: Péter L. Erdős
MaRDI profile type: Publication
full work available at URL: 0097-3165(86)90063-4
OpenAlex ID: W2088742261
cites work: Erdös–Ko–Rado Theorem—22 Years Later
cites work: INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
cites work: Q4184835
cites work: Q4196436
cites work: Intersection theorems for systems of finite vector spaces
cites work: The exact bound in the Erdős-Ko-Rado theorem
DBLP publication ID: journals/jct/FranklW86
description: scientific article; zbMATH DE number 3985272