The spectrum of minimal defining sets of some Steiner systems
type: Item
instance of: scholarly article
title: The spectrum of minimal defining sets of some Steiner systems
zbMATH Open document ID: 1027.51006
DOI: 10.1016/S0012-365X(02)00474-0
author: Brenton D. Gray
author: Tony Moran
author: Anne Penfold Street
author: Rudolf Mathon
published in: Discrete Mathematics
publication date: 2003-03-16T00:00:00Z
review text: Defining sets of a design were introduced by \textit{K. Gray} [Util. Math. 38, 97-103 (1990; Zbl 0726.05014)] as sets of blocks which are subsets of a unique design; they are said minimal if they properly contain no other defining set. In the paper under review the set of sizes of the minimal defining sets of a design is called its ``spectrum''. The authors investigate the bounds of the spectrum of Steiner systems and, in particular, the case of Steiner triple system of the points and lines of the projective space \(PG(3,2)\); they also point out some open questions concerning the Steiner triple system associated with \(PG(n,2)\) .
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1882223
zbMATH Keywords: defining sets
zbMATH Keywords: Steiner systems
zbMATH Keywords: projective geometries over GF(2)
reviewed by: Bambina Larato
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00474-0
OpenAlex ID: W2033776284
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description: scientific article; zbMATH DE number 1882223