Block disjoint difference families for Steiner triple systems: \(v\equiv 3 \mod 6\)
type: Item
instance of: scholarly article
title: Block disjoint difference families for Steiner triple systems: \(v\equiv 3 \mod 6\)
zbMATH Open document ID: 0996.05013
DOI: 10.1016/S0378-3758(02)00204-5
author: J. H. Dinitz
author: Nabil Shalaby
published in: Journal of Statistical Planning and Inference
publication date: 2002-09-18T00:00:00Z
review text: Given a group \(G\) of order \(v\), a family of pairwise disjoint \(k\)-tuples of elements from \(G\) is a block disjoint \((v,k,\lambda)\) difference family if the collection of orbits of the \(k\)-tuples under the action of \(G\) form a BIBD\((v,k,\lambda)\). In 1997 the first author and \textit{P. Rodney} [Util. Math. 52, 153-160 (1997; Zbl 0892.05012)] showed that there exists a block disjoint \((v,3,1)\) difference family for all \(v \equiv 1 {\pmod 6}\). In this companion paper the authors use similar techniques to establish the existence of a cyclic block disjoint \((v,3,1)\) difference family for all \(v \equiv 3 {\pmod 6}\) with \(v \geq 3\) and \(v \neq 9\). In the case \(v = 9\), there is a \(1\)-rotational block disjoint \((9,3,1)\) difference family (with point set \(Z_8 \cup \infty\)), namely \(\{\{\infty,0,4\},\{1,2,7\}\}\). Combining this with the result from the companion paper, it is established that a block disjoint \((v,3,1)\) difference family exists for all \(v \equiv 1,3 {\pmod 6}\) with \(v \geq 3\).
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 1802341
zbMATH Keywords: Steiner triple system
zbMATH Keywords: difference family
reviewed by: Peter B. Gibbons
MaRDI profile type: Publication
cites work: Q4338936
cites work: Q4378180
full work available at URL: s0378-3758(02)00204-5
OpenAlex ID: W1491894411
description: scientific article; zbMATH DE number 1802341