A309088 a(n) is the number of isotopy classes of order n Latin squares that produce a unique determinant.

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.

Links

Table of n, a(n) for n=1..7.

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

Index entries for sequences related to determinants

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

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

Alvaro R. Belmonte, Eugene Fiorini, Peterson Lenard, Froylan Maldonado, Sabrina Traver, Wing Hong Tony Wong, Jul 11 2019

Status

approved