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Antiflexible Latin directed triple systems

Andrew R. Kozlik (2015)

Commentationes Mathematicae Universitatis Carolinae

It is well known that given a Steiner triple system one can define a quasigroup operation · upon its base set by assigning x · x = x for all x and x · y = z , where z is the third point in the block containing the pair { x , y } . The same can be done for Mendelsohn triple systems, where ( x , y ) is considered to be ordered. But this is not necessarily the case for directed triple systems. However there do exist directed triple systems, which induce a quasigroup under this operation and these are called Latin directed triple systems....

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