Intersection theorems for vector spaces
type: Item
instance of: scholarly article
title: Intersection theorems for vector spaces
zbMATH Open document ID: 0577.15002
DOI: 10.1016/S0195-6698(85)80009-3
author: Peter Frankl
author: Ron Graham
published in: European Journal of Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: Let \(b\) be a positive integer, \({\mathcal F}=\{F_1,\ldots, F_m\}^a \) collection of \(k\)-dimensional subspaces of an \(n\)-dimensional vector space over a finite field \(K\). Let there exist numbers \(\mu_1,\ldots, \mu_s\) with \(k\not\equiv \mu_i \pmod b\), \(1\leq t\leq s\), and for all \(i,j\) with \(1\leq i<j\leq m\) and some \(t\), \(\dim \vert F_i\cap F_j\vert \equiv \mu_t \pmod b\). Then \(\vert\mathcal F\vert \leq \left[ \begin{matrix} n \\ s\end{matrix} \right]_q\), with \[ \left[ \begin{matrix} n\\ s\end{matrix} \right]_ q = \prod_{0\leq i<s} \frac{q^{n-i}-1} {q^{t-i}-1}\quad\text{and}\quad \vert K\vert =q. \] Applying this a constructive lower bound is given for the Ramsey number \(R(k,k)\).
reviewed by: Gerard Sierksma
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 3922867
zbMATH Keywords: number of subspaces
zbMATH Keywords: finite field
zbMATH Keywords: Ramsey number
MaRDI profile type: Publication
cites work: INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
cites work: Intersection theorems with geometric consequences
cites work: On hypergraphs without two edges intersecting in a given number of vertices
cites work: Forbidding just one intersection
cites work: Q3903002
cites work: Q4196436
cites work: Intersection theorems for systems of finite vector spaces
cites work: A simple proof of the Erdős-Chao Ko-Rado theorem
description: scientific article; zbMATH DE number 3922867