The classification of flats in \(\text{PG}(\mathbf{9,2})\) which are external to the Grassmannian \({\mathcal G}_{\mathbf{1,4,2}}\)
type: Item
instance of: scholarly article
title: The classification of flats in \(\text{PG}(\mathbf{9,2})\) which are external to the Grassmannian \({\mathcal G}_{\mathbf{1,4,2}}\)
zbMATH Open document ID: 1077.51001
author: Johannes Maks
author: Neil Gordon
author: Ron Shaw
published in: Designs, Codes and Cryptography
publication date: 2005-02-28T00:00:00Z
review text: In this paper the authors are concerned with those flats in the projective space \(\text{PG}(9, 2)= \mathbb{P}(V(5, 2)\wedge V(5, 2))\), which are external to the Grassmannian \(\mathcal H\) arising from the 155 lines of the projective space \(\text{PG}(4, 2)= \mathbb{P}(V(5, 2))\). On the basis of three unpublished papers, which are available via the internet, a complete classification of all external \(k\)-flats is given. Apart from the trivial class of \(0\)-flats there are nine further classes. For \(k= 1,3,4\) there are two classes and in the case \(k= 2\) there are three different types. In any case each class is an orbit under the induced action of the linear group \(\text{GL}(5, 2)\) on the projective space \(\text{PG}(9,2)\).
reviewed by: Udo Ott
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 2139254
zbMATH Keywords: Grassmannian
zbMATH Keywords: external flats
zbMATH Keywords: \(\text{GL}(5,2)\)
MaRDI profile type: Publication
full work available at URL: s10623-004-4855-6
OpenAlex ID: W2016091231
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DOI: 10.1007/S10623-004-4855-6
description: scientific article; zbMATH DE number 2139254