Maximally nonassociative quasigroups
This data was produced for my project with Ales Drapal where we looked
at quasigroups with the fewest number of associative triples. An
associative triple (x,y,z) is one for which (xy)z=x(yz). It is not
hard to show that every quasigroup of order n has at least n
associative triples. Also, to achieve exactly n, the quasigroup must
be idempotent, which means that the n triples are all of the form
For our first paper on the subject we had a few theorems which relied
on computations. Here I give the data backing up our claims for
Theorem 4.6 (2.8Mb).
I'll also take this chance to give a bunch of maximally nonassociative quasigroups that I found during our investigations. In each case these are just examples, not exhaustive enumerations. The examples that I present are not isomorphic to each other or to the transpose (opposite) of another example.
If you want to know what format these files are in, it is my
usual latin squares format.
Back to data homepage.