A000519

[Brendan McKay]

* Jim Nastos <nastos at cs.ualberta.ca> [030419 07:03]:
> 
>   If I can divert from this question for a moment...
> There are a few sequences numbering the equivalence classes of latin 
> squares for various definitions of equivalence... How come there is no 
> sequence for the number latin squares up to isomorphism, where an 
> isomorphism here is just any permutation of labels.

Right, that type of equivalence has been mentioned in the literature
but I never saw any counts for it.

>   If I'm not mistaken, don't distinct transversal designs map to distinct 
> latin squares (where the meaning "distinct latin squares" is in the sense 
> above.) The encyclopedia seems to have no data counting transversal 
> designs at all.

I don't see this mapping.  Is it just for particular values of
k and lambda?  Please expand.

Wendy Myvold, Alison Meynert and myself have found all the Latin
squares up to order 10 with non-trivial symmetries.  Together
with the known counts of labelled squares, this allows us to
infer the number of equivalence classes according to many types
of equivalence.  We didn't do the type of equivalence you mention
but it wouldn't be hard, and an application like you suggest would
be the perfect excuse.  Btw, to reduce the chance of wrong numbers
getting out, we are holding them back until we finished all our
checking computations.  Not long now.

Brendan.