Homogeneous embeddings of disjoint Mendelsohn triple systems
type: Item
instance of: scholarly article
title: Homogeneous embeddings of disjoint Mendelsohn triple systems
zbMATH Open document ID: 0852.05023
DOI: 10.1016/0378-3758(95)00078-X
author: Wensong Chu
published in: Journal of Statistical Planning and Inference
publication date: 1996-09-05T00:00:00Z
review text: Let \({\mathcal S}_X= \{(X, {\mathcal A}_i)\mid 1\leq i\leq n\}\) and \({\mathcal S}_Y= \{(Y, {\mathcal B}_i)\mid 1\leq i\leq n\}\) be two sets of pairwise disjoint Mendelsohn triple systems of order \(v\) and \(u\), respectively. The set \({\mathcal S}_X\) is homogeneously embeddable in \({\mathcal S}_Y\) if for each \(i\) with \(1\leq i\leq n\), the system \((X, {\mathcal A}_i)\) is embeddable in \((Y, {\mathcal B}_i)\). It is proved that if \(u- v\equiv 1\) or \(2\pmod 3\), then \(n\) disjoint Mendelsohn triple systems of order \(v\) can be homogeneously embedded in \(n\) disjoint Mendelsohn triple systems of order \(u\) if and only if \(u, v\equiv 0\) or \(1\pmod 3\), \(u\geq 2v+ 1\), \(v\geq 3\), \(v\neq 6\), for any \(n\) such that \(1\leq n\leq v- 2\).
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 906652
zbMATH Keywords: homogeneous embedding
zbMATH Keywords: Mendelsohn triple systems
reviewed by: Jozef Širáň
MaRDI profile type: Publication
cites work: Embeddings of Steiner triple systems
cites work: Q3949068
cites work: Q4309132
full work available at URL: 0378-3758(95)00078-x
OpenAlex ID: W2057218577
description: scientific article; zbMATH DE number 906652