Self-orthogonal Mendelsohn triple systems
type: Item
instance of: scholarly article
title: Self-orthogonal Mendelsohn triple systems
zbMATH Open document ID: 0842.05008
DOI: 10.1016/S0097-3165(96)80002-1
author: Yanyan Li
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-05-13T00:00:00Z
review text: A Mendelsohn triple system of order \(v\), briefly \(\text{MTS}(v)\), is a pair \((X, B)\) where \(X\) is a \(v\)-set of points and \(B\) is a collection of triples \((a, b, c)\) that contain ordered pairs \((a, b)\), \((b, c)\), and \((c, a)\) such that every ordered pair of distinct points occurs in exactly one tripe of \(B\). One can construct a latin square of order \(v\) from \(\text{MTS}(v)\) and if the latin square is orthogonal to its transpose, then the \(\text{MTS}(v)\) is said to be self-orthogonal, denoted by \(\text{SOMTS}(v)\). In this paper it is shown that a \(\text{SOMTS}(v)\) exists for all \(v\equiv 0\pmod 3\), except possibly for \(v= 18\).
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 842847
zbMATH Keywords: quasigroup
zbMATH Keywords: pairwise balanced design
zbMATH Keywords: Mendelsohn triple system
zbMATH Keywords: latin square
reviewed by: D. Raghavarao
MaRDI profile type: Publication
cites work: Self-orthogonal semisymmetric quasigroups
cites work: Q4026145
cites work: Q3686719
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cites work: Existence of orthogonal Latin squares with aligned subsquares
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full work available at URL: s0097-3165(96)80002-1
OpenAlex ID: W4213236732
description: scientific article; zbMATH DE number 842847