The minimum size of a finite subspace partition
type: Item
instance of: scholarly article
title: The minimum size of a finite subspace partition
zbMATH Open document ID: 1223.51011
published in: Linear Algebra and its Applications
publication date: 2011-07-15T00:00:00Z
review text: Let \(\sigma_q(n,t)\) denote the minimal size in a subspace partition of \(PG(n,q)\) in which the largest subspace has dimension \(t\). In this paper it is proved that \(\sigma_q(n,t)=q^{t+1}+1\) for \(n<2t+2\) and \(\sigma_q(2t+2,t)=q^{t+2}+q^{[t/2]+1}+1\) (Corollary 7). Moreover, the minimal size of a maximal partial \(t\)-spread in \(PG(3t+2,q)\) is given by \(\sigma_q(2t+2,t)\) (Theorem 11).
Mathematics Subject Classification ID: 51E23
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 51E14
zbMATH DE Number: 5924532
zbMATH Keywords: subspace partition
zbMATH Keywords: partial \(t\)-spreads
author: E. Năstase
author: Papa A. Sissokho
reviewed by: Alexandre A. Makhnev
MaRDI profile type: Publication
full work available at URL: j.laa.2011.03.006
OpenAlex ID: W1994347381
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DOI: 10.1016/J.LAA.2011.03.006
description: scientific article; zbMATH DE number 5924532