The spectrum of nested Steiner triple systems
type: Item
instance of: scholarly article
title: The spectrum of nested Steiner triple systems
zbMATH Open document ID: 0583.05015
DOI: 10.1007/BF02582943
published in: Graphs and Combinatorics
publication date: 1985-01-01T00:00:00Z
review text: A Steiner triple system of order v (STS(v)) is nested if it is possible to add a point to each block and obtain a BIBD(v,4,2). Clearly it is necessary that \(v\equiv 1(mod 6)\). The author points out that, in a sequence of papers, it had been shown that a nested STS(v) is possible whenever \(v\equiv 1(mod 6)\) but with perhaps a few exceptions. Using an unpublished idea of J. Q. Longyear, the author gives a very short and simple proof of the existence of nested STS(v) for all \(v\equiv 1(mod 6)\).
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 3933089
zbMATH Keywords: balanced incomplete block design
zbMATH Keywords: Steiner triple system
zbMATH Keywords: nested
zbMATH Keywords: BIBD
author: D. R. Stinson
reviewed by: Katherine Heinrich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3933089