Distributive and Anti-distributive Mendelsohn Triple Systems

被引：4

作者：

Donovan, Diane M. ^{[1
]}

Griggs, Terry S. ^{[2
,3
]}

McCourt, Thomas A. ^{[4
]}

Oprsal, Jakub ^{[5
]}

Stanovsky, David ^{[5
]}

机构：

[1] Univ Queensland, Ctr Discrete Math & Comp, St Lucia, Qld 4072, Australia

[2] Open Univ, Dept Math & Stat, Walton Hall, Milton Keynes MK7 6AA, Bucks, England

[3] Univ Plymouth, Sch Comp & Math, Plymouth PL4 8AA, Devon, England

[4] Univ Bristol, Heilbronn Inst Math Res, Univ Walk, Bristol BS8 1TW, Avon, England

[5] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Sokolovska 83, Prague 18675 8, Czech Republic

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2016年 / 59卷 / 01期

关键词：

Mendelsohn triple system; quasigroup; distributive; Moufang loop; Loeschian numbers; MITRE;

D O I：

10.4153/CMB-2015-053-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：36 / 49

页数：14

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