Distributive and anti-distributive Mendelsohn triple systems

Donovan, Diane M., Griggs, Terry S., McCourt, Thomas A., Oprsal, Jakub and Stanovsky, David (2016) Distributive and anti-distributive Mendelsohn triple systems. Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 59 1: 36-49. doi:10.4153/CMB-2015-053-2

Author Donovan, Diane M.
Griggs, Terry S.
McCourt, Thomas A.
Oprsal, Jakub
Stanovsky, David
Title Distributive and anti-distributive Mendelsohn triple systems
Journal name Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques   Check publisher's open access policy
ISSN 0008-4395
Publication date 2016-03
Year available 2015
Sub-type Article (original research)
DOI 10.4153/CMB-2015-053-2
Open Access Status Not Open Access
Volume 59
Issue 1
Start page 36
End page 49
Total pages 14
Place of publication Toronto, ON, Canada
Publisher University of Toronto Press * Journals Division
Collection year 2017
Language eng
Abstract We prove that the existence spectrum of Mendelsohn triple systems whose associated quasigroups satisfy distributivity corresponds to the Loeschian numbers, and provide some enumeration results. We do this by considering a description of the quasigroups in terms of commutative Moufang loops. In addition we provide constructions of Mendelsohn quasigroups that fail distributivity for as many combinations of elements as possible. These systems are analogues of Hall triple systems and anti-mitre Steiner triple systems respectively.
Keyword Mendelsohn triple system
Moufang loop
Loeschian numbers
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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