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

1,2

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.

Links

Table of n, a(n) for n=1..9.

Peterson Lenard, Greatest Common Divisor of all determinants

Brendan McKay, Combinatorial Data

Example

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.

Prog

(Sage) # See Peterson Lenard link

Crossrefs

Cf. A301371, A308853, A309088, A309258.

Sequence in context: A241628 A056319 A056310 * A308853 A309257 A135371

Adjacent sequences: A309256 A309257 A309258 * A309260 A309261 A309262

Keyword

nonn,hard,more

Author

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

Extensions

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

Status

approved