On large sets of hybrid triple systems
type: Item
instance of: scholarly article
title: On large sets of hybrid triple systems
zbMATH Open document ID: 0855.05022
DOI: 10.1016/0378-3758(95)00082-8
published in: Journal of Statistical Planning and Inference
publication date: 1996-09-05T00:00:00Z
review text: An oriented triple system \(\mathcal B\) on a \(v\)-set \(X\) is called a hybrid triple system and denoted by \(\text{HTS}(v, \lambda)\) if it contains both cyclic and transitive triples such that each ordered pair of distinct elements is contained in exactly \(\lambda\) triples of \(\mathcal B\). If all the cyclic and transitive triples from \(X\) can be partitioned into \(\bigcup_i {\mathcal B}_i\) such that each \((X, {\mathcal B}_i)\) is an \(\text{HTS}(v, \lambda)\), then \(\{(X, {\mathcal B}_i)\}_i\) is called a large set of pairwise disjoint hybrid triple systems and denoted by \(\text{LHKTS}(v, \lambda)\). In this paper, the authors determine necessary and sufficient conditions for the existence of \(\text{LHKTS}(v, \lambda)\).
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 906656
zbMATH Keywords: oriented triple system
zbMATH Keywords: hybrid triple system
author: Qingde Kang
author: Jianguo Lei
reviewed by: Esther R. Lamken
MaRDI profile type: Publication
full work available at URL: 0378-3758(95)00082-8
OpenAlex ID: W2079148914
cites work: Q4004080
cites work: Q4309132
cites work: A completion of the spectrum for large sets of disjoint transitive triple systems
cites work: Q3329483
cites work: Large sets with holes
description: scientific article; zbMATH DE number 906656