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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Froylan Maldonado, Sage code Brendan McKay, Latin squares Brendan McKay, Order 4 isotopic classes Brendan McKay, Order 5 isotopic classes Brendan McKay, Order 6 isotopic classes Brendan McKay, Order 7 isotopic classes 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 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 Cf. A301371, A308853. Sequence in context: A050971 A118855 A009515 * A070944 A278836 A227447 Adjacent sequences:  A309085 A309086 A309087 * A309089 A309090 A309091 KEYWORD nonn,hard,more AUTHOR STATUS approved

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Last modified October 20 16:05 EDT 2019. Contains 328268 sequences. (Running on oeis4.)