McKay, Brendan; Wanless, Ian
We count all latin cubes of order n < 6 and latin hypercubes of order n < 5 and dimension d < 5. We classify these (hyper)cubes into isotopy classes and paratopy classes (main classes). For the same values of n and d we classify all d-ary quasigroups of order n into isomorphism classes and also count them according to the number of identity elements they possess (meaning we have counted the d-ary loops). We also give an exact formula for the number of (isomorphism classes of) d-ary quasigroups...[Show more]
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