Classification of partitions of all triples on ten points into copies of Fano and affine planes
type: Item
instance of: scholarly article
title: Classification of partitions of all triples on ten points into copies of Fano and affine planes
zbMATH Open document ID: 1148.05014
author: Anne Penfold Street
author: Greg Gamble
author: Rudolf Mathon
published in: Discrete Mathematics
publication date: 2008-05-29T00:00:00Z
review text: In two recent papers the authors have studied partitions of the full set of triples chosen from a \(v\)-set into copies of the Fano plane PG(2, 2) or copies of the affine plane AG(2, 3) or copies of both. The Fano partitions for \(v = 8\) and the affine partitions for \(v = 9, 10\) have been fully classified. In the paper under review it is shown that there are precisely 22 isomorphism classes of mixed partitions for \(v = 10\), and it is observed that this completes the classification for \(v\) at most 10. It should be noted that no Fano, affine, or mixed partition exists for \(v\) less than or equal to 7 or for \(v = 11\). For \(v\) greater than or equal to 12 no complete classification seems infeasible.
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 5280715
zbMATH Keywords: triple systems
zbMATH Keywords: Fano partitions
zbMATH Keywords: affine partitions
zbMATH Keywords: mixed partitions
reviewed by: Gary L. Ebert
MaRDI profile type: Publication
full work available at URL: j.disc.2006.06.043
OpenAlex ID: W2029365998
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DOI: 10.1016/J.DISC.2006.06.043
description: scientific article; zbMATH DE number 5280715