Intersections of Steiner systems S(3,4,v) with \(v=5\cdot 2^ n\)
type: Item
instance of: scholarly article
title: Intersections of Steiner systems S(3,4,v) with \(v=5\cdot 2^ n\)
zbMATH Open document ID: 0574.51014
DOI: 10.1007/BF01220481
published in: Journal of Geometry
publication date: 1985-01-01T00:00:00Z
review text: In the paper the block intersection problem for Steiner quadruple systems (SQS) having orders \(v=5\cdot 2^ n\), \(n\geq 2\) is examined. The main result is \(I_ v-\{q_ v-17\}\subset J(v),\) for all \(v=5\cdot 2^ n\), \(n\geq 2\), where \(q_ v=v\cdot (v-1)\cdot (v-2)/24\), \(I_ v=\{0,1,2,...,q_ v-I4,q_ v-I2,q_ v-8,q_ v\}\) for \(v\geq 8\), and \(J(v)=\{k:\exists SQS(v),(Q,q_ 1),(Q,q_ 2)\) such that \(| q_ 1\cap q_ 2| =k\}\).
reviewed by: M.Kratko
Mathematics Subject Classification ID: 51E10
zbMATH DE Number: 3917115
zbMATH Keywords: block intersection problem
zbMATH Keywords: Steiner quadruple systems
author: Mario Gionfriddo
MaRDI profile type: Publication
cites work: An Updated Bibliography and Survey of Steiner Systems
cites work: Q3937414
cites work: Some Results on Partial Steiner Quadruple Systems
cites work: On the set \(J(v)\) for Steiner quadruple systems of order \(v=2^ n\) with \(n\geq 4\)
cites work: Q3671188
cites work: Construction of Steiner quadruple systems having a prescribed number of blocks in common
cites work: Q4749850
cites work: On Quadruple Systems
cites work: Intersections among Steiner systems
cites work: Steiner Triple Systems Having a Prescribed Number of Triples in Common
cites work: Steiner quadruple systems - a survey
cites work: Q3347896
cites work: Intersection Properties of Steiner Systems
full work available at URL: https://doi.org/10.1007/bf01220481
OpenAlex ID: W2007111588
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description: scientific article; zbMATH DE number 3917115