A309258 a(n) is the number of distinct absolute values of determinants of order n Latin squares.

1, 1, 1, 3, 6, 197, 3684, 159561

Offset: 1

Author

Alvaro R. Belmonte, Eugene Fiorini, Peterson Lenard, Froylan Maldonado, Sabrina Traver, Wing Hong Tony Wong, Jul 19 2019

Keywords

• nonn
• hard
• more

Comments

We apply every symbol permutation on the representatives of isotopic classes to generate Latin squares of order n and calculated the determinants. We then obtained the absolute values of the determinants and removed duplicates.

These results are based on work supported by the National Science Foundation under grants numbered DMS-1852378 and DMS-1560019.

a(9) >= 1747706. - Hugo Pfoertner, Nov 20 2019

Examples

			For n = 5, the set of absolute values of determinants is {75, 825, 1200, 1575, 1875, 2325}, so a(5) = 6.
		

Links

• Froylan Maldonado, Code
• Brendan McKay, Latin squares
• Hugo Pfoertner, 8X8 Latin squares: Illustration of occurrence counts of determinant values, 5.7 MB, zoom in to see details (2019).
• Hugo Pfoertner, Occurrence counts of determinant values for n=1..8, zipped (2019).

Crossrefs

Cf. A040082, A088021, A301371, A308853, A309984, A309985.

Programs

Sage

# See Maldonado link.

Extensions

a(8) from Hugo Pfoertner, Aug 26 2019