A309089 a(n) is the number of absolute values of determinants that come from a unique isotopy class of order n Latin squares.

1, 1, 1, 2, 5, 85, 124

Offset: 1

Author

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

Keywords

• nonn
• hard
• more

Comments

We apply every symbol permutation on the representatives of isotopic classes to generate Latin square 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.

Examples

			For n=4, the determinants 80 and 160 are produced by a unique isotopic class which has [[1, 2, 3, 4], [2, 4, 1, 3], [3, 1, 4, 2], [4, 3, 2, 1]] as a representative. All other determinants are produced by multiple isotopic classes. Therefore a(4)=2.
		

Links

• Peterson Lenard, Number of unique determinants
• Brendan McKay, Latin squares

Crossrefs

Cf. A301371, A308853, A309088.

Programs

Sage

# See Maldonado link