Semisymmetric Latin Squares
This data was produced in my collaboration with Brendan McKay for the paper
"Enumeration of Latin squares with conjugate symmetry".
A semisymmetric Latin square is one that is equal to 3
of its conjugates (also known as parastrophes). That means that
the set of (row,column,symbol) triples is unchanged by cyclic permutation of each triple.
We start with catalogues of semisymmetric Latin squares up to isomorphism:
...and the species that contain semisymmetric Latin squares:
Next, isomorphism classes of idempotent semisymmetric Latin squares:
Next, isomorphism classes of diagonal semisymmetric Latin squares:
Next, isomorphism classes of semisymmetric loops (reduced LS):
We did also generate the
semisymmetric Latin squares of order 11, the idempotent
semisymmetric Latin squares of order 12, the diagonal semisymmetric
Latin squares of order 12 and the semisymmetric loops of order 12.
In each case, 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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