Colourings with fixed congruence in finite projective planes
type: Item
instance of: scholarly article
title: Colourings with fixed congruence in finite projective planes
zbMATH Open document ID: 0884.51007
DOI: 10.1007/BF01229572
author: Sandro Rajola
published in: Journal of Geometry
publication date: 1997-08-28T00:00:00Z
review text: The author investigates nontrivial partitions of the point set of a finite projective plane of order \(q\) such that each partition class meets each line in \(d \bmod h\) points, for some fixed natural numbers \(d\) and \(h\), \(h\geq 2\). The main results are that \(h\neq q\), that \(q\) cannot be prime, nor a product of two distinct odd primes, every partition class is a blocking set, and (hence) the number of partition classes does not exceed \(q-1\). The author also investigates the situation for planes of small order. For \(q=4\), a complete classification is easily obtained, for \(q=8, 9, 12, 16, 18\), restrictions on the pairs \((d,h)\) are obtained, along with partial classification results.
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 1053896
zbMATH Keywords: Baer subspheres
zbMATH Keywords: finite projective plane
zbMATH Keywords: blocking set
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
cites work: Q3236264
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full work available at URL: https://doi.org/10.1007/bf01229572
OpenAlex ID: W2089986607
description: scientific article; zbMATH DE number 1053896