Totally Symmetric Latin Squares

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

A totally symmetric Latin square is one that is equal to all 6 of its conjugates (also known as parastrophes). That means that the set of (row,column,symbol) triples can be thought of as unordered triples!

Here we give catalogues of totally symmetric Latin squares up to isomorphism.

order 2
order 3
order 4
order 5
order 6
order 7
order 8
order 9
order 10
order 11
order 12 (gzipped file)
order 13 (gzipped file)

We did also generate the totally symmetric Latin squares of order 14 and 15. There are too many to present in this format, but they are available on request.

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

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