Geodesic
Distributive and Anti-distributive Mendelsohn Triple Systems
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 36-49

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DOI

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 asmany combinations of elements as possible. These systems are analogues of Hall triple systems and anti-mitre Steiner triple systems respectively.
DOI : 10.4153/CMB-2015-053-2
Mots-clés : 20N05, 05B07, Mendelsohn triple system, quasigroup, distributive, Moufang loop, Loeschian numbers 
Donovan, Diane M.; Griggs, Terry S.; McCourt, Thomas A.; Opršal, Jakub; Stanovský, David. Distributive and Anti-distributive Mendelsohn Triple Systems. Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 36-49. doi: 10.4153/CMB-2015-053-2
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     author = {Donovan, Diane M. and Griggs, Terry S. and McCourt, Thomas A. and Opr\v{s}al, Jakub and Stanovsk\'y, David},
     title = {Distributive and {Anti-distributive} {Mendelsohn} {Triple} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {36--49},
     year = {2016},
     volume = {59},
     number = {1},
     doi = {10.4153/CMB-2015-053-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-053-2/}
}
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%A McCourt, Thomas A.
%A Opršal, Jakub
%A Stanovský, David
%T Distributive and Anti-distributive Mendelsohn Triple Systems
%J Canadian mathematical bulletin
%D 2016
%P 36-49
%V 59
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