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A309088
a(n) is the number of isotopy classes of order n Latin squares that produce a unique determinant.
5
1, 1, 1, 1, 2, 8, 25
OFFSET
1,5
COMMENTS
We apply every symbol permutation on the representatives of isotopic classes to generate Latin squares of order n and calculate the determinants.
These results are based upon work supported by the National Science Foundation under the grants numbered DMS-1852378 and DMS-1560019.
EXAMPLE
For n=5, the only isotopic class that produces determinants 825, 1875, and 2325 is the one with [[1, 2, 3, 4, 5] [2, 3, 5, 1, 4], [3, 5, 4, 2, 1], [4, 1, 2, 5, 3], [5, 4, 1, 3, 2]] as a representative, and the only isotopic class that produces determinants 1200 and 1575 is the one with [[1, 2, 3, 4, 5], [2, 4, 1, 5, 3], [3, 5, 4, 2, 1], [4, 1, 5, 3, 2], [5, 3, 2, 1, 4]] as a representative.
Therefore, a(5)=2 since there are two isotopic classes that produce determinants that are unique to that isotopic class.
PROG
(Sage) See Maldonado link.
CROSSREFS
Sequence in context: A050971 A118855 A009515 * A070944 A278836 A227447
KEYWORD
nonn,hard,more
STATUS
approved