Intersection problem of Steiner systems S(3,4,2v)
type: Item
instance of: scholarly article
title: Intersection problem of Steiner systems S(3,4,2v)
zbMATH Open document ID: 0636.05014
DOI: 10.1016/0012-365X(87)90175-0
author: Hung-Lin Fu
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: This paper gives an almost complete solution to the intersection problem for Steiner quadruple systems of orders \(v\equiv 4\) or 8 (mod 12). The intersection problem remains open for systems of orders \(v\equiv 2\) or 10 (mod 12). The two main results are: If a complete solution for the cases \(v\in \{16,20,28\}\) is found then this implies a complete solution for all \(v\equiv 4\) or 8 (mod 12). For \(v\equiv 4\) or 8 (mod 12), the intersection problem is solved with three possible exceptions for each value of v. The techniques used are recursive, and rely heavily on embedding techniques for Steiner quadruple systems.
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 51E10
zbMATH DE Number: 4035850
zbMATH Keywords: intersection problem
zbMATH Keywords: Steiner quadruple systems
MaRDI profile type: Publication
cites work: On embedding incomplete symmetric Latin squares
cites work: On the finite completion of partial latin cubes
cites work: Q3754643
cites work: Q3731613
cites work: Q3829555
cites work: Construction of Steiner quadruple systems having a prescribed number of blocks in common
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: Intersections of Steiner systems S(3,4,v) with \(v=5\cdot 2^ n\)
cites work: Q4749850
cites work: Q3347896
cites work: On Quadruple Systems
cites work: A general recursive construction for quadruple systems
cites work: Q4186330
cites work: A Note on One-Factorizations Having a Prescribed Number of Edges in Common
full work available at URL: 0012-365x(87)90175-0
OpenAlex ID: W1976337561
description: scientific article; zbMATH DE number 4035850