A309259 a(n) is the greatest common divisor of the determinants of order n Latin squares.

1, 3, 18, 80, 75, 63, 196, 144, 405

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 calculate the determinants. We then compute the greatest common divisor of the values obtained.

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 set of absolute values of the determinants is {0, 80, 160}, so the greatest common divisor of the determinants is 80. Therefore, a(4)=80.
		

Links

• Peterson Lenard, Greatest Common Divisor of all determinants
• Brendan McKay, Combinatorial Data

Crossrefs

Cf. A301371, A308853, A309088, A309258.

Programs

Sage

# See Peterson Lenard link

Extensions

a(8), a(9) from Hugo Pfoertner, Sep 02 2019