A special class of nested Steiner triple systems
type: Item
instance of: scholarly article
title: A special class of nested Steiner triple systems
zbMATH Open document ID: 0851.05023
DOI: 10.1016/0012-365X(94)00247-G
published in: Discrete Mathematics
publication date: 1996-11-21T00:00:00Z
review text: A nested Steiner triple system of order \(v\), \(\text{NSTS}(v)\), is an \(\text{STS}(v)\) with a point added to each block in such a way that the resulting blocks form a 2-\((v, 4, 2)\) design. The author defines a partitionable nested triple system to be an \(\text{NSTS}(v)\) whose blocks can be partitioned into two 2-\((v, 4, 1)\) designs. He proves, by construction, that a partitionable \(\text{NSTS}(v)\) exists iff \(v\equiv 1\pmod{12}\). The general construction uses group divisible designs and special cases are dealt with by ad hoc constructions.
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 897589
zbMATH Keywords: nested Steiner triple system
zbMATH Keywords: block
zbMATH Keywords: design
zbMATH Keywords: triple system
author: Darryn Bryant
MaRDI profile type: Publication
cites work: Optimal packings of \(K_4\)'s into a \(K_n\)
cites work: Q3323963
cites work: Q3222204
cites work: The spectrum of nested Steiner triple systems
Wikidata QID: Q127878206
full work available at URL: 0012-365x(94)00247-g
OpenAlex ID: W2047247417
description: scientific article; zbMATH DE number 897589