Large sets of extended directed triple systems with even orders
type: Item
instance of: scholarly article
title: Large sets of extended directed triple systems with even orders
zbMATH Open document ID: 1189.05033
author: Yuanyuan Liu
author: Qingde Kang
published in: Discrete Mathematics
publication date: 2009-12-15T00:00:00Z
review text: Let \(X\) be a finite set of cardinality \(v\). An extended directed triple \((x,y,z)\) is a set of ordered pairs \((x,y)\), \((y,z)\), \((x,z)\) of not necessarily distinct elements of \(X\). An extended directed triple system \(EDTS(v)\) is a pair \((X,\mathcal A)\), where \(\mathcal A\) is a set of extended directed triples such that each ordered pair of elements belongs to exactly one extended triple. A large set \(LEDTS(v)\) of \(EDTS(v)\) is a collection \( \{(X,\mathcal A_k)\}_k\), where \(X\) is a \(v\)-set and each extended directed triple of \(X\) belongs to exactly one system \((X,\mathcal A_k)\). The authors prove that there exist \(LEDTS(v)\) for all even values, with the exception of \(v=4\).
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 5648212
zbMATH Keywords: extended directed triple
zbMATH Keywords: extended directed triple system
zbMATH Keywords: large set
reviewed by: Ludovit Niepel
MaRDI profile type: Publication
full work available at URL: j.disc.2009.06.025
OpenAlex ID: W1973536195
cites work: Extended cyclic triple systems
cites work: Q4173368
cites work: Extended directed triple systems
cites work: EXTENDED DIRECTED TRIPLE SYSTEMS WITH A GIVEN AUTOMORPHISM
cites work: Extended triple systems
cites work: A new existence proof for large sets of disjoint Steiner triple systems
cites work: Candelabra systems and designs
cites work: The spectrum for overlarge sets of directed triple systems
cites work: The spectrum for large sets of pure directed triple systems
DOI: 10.1016/J.DISC.2009.06.025
description: scientific article; zbMATH DE number 5648212