Symmetric Latin Squares

This data was produced in my collaboration with Brendan McKay for the paper "Enumeration of Latin squares with conjugate symmetry".

A symmetric Latin square is one that is equal to its matrix transpose. That means that the set of (row,column,symbol) triples is unchanged by swapping the first two coordinates.

We start with catalogues of all reduced symmetric Latin squares:

Then symmetric Latin squares up to isomorphism:

...and the rrs-isotopism classes of symmetric Latin squares...

...and the species that contain symmetric Latin squares:

order 8
For other orders up to 9, just use the rrs-isotopism class representatives above.

Next, isomorphism classes of unipotent reduced symmetric Latin squares:

order 2
order 4
order 6
order 8
order 10
(There are none of odd orders).

Next, isomorphism classes of commutative loops (symmetric reduced LS):

We did also generate larger orders in each case, but there are too many to present in this format. If you need something that's mentioned in the paper, then ask!

If you want to know what format these files are in, it is my usual latin squares format.

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