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

1,4

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

Links

Table of n, a(n) for n=1..8.

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).

Example

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

Prog

(Sage) # See Maldonado link.

Crossrefs

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

Sequence in context: A019437 A365505 A291982 * A163423 A291126 A083149

Adjacent sequences: A309255 A309256 A309257 * A309259 A309260 A309261

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) from Hugo Pfoertner, Aug 26 2019

Status

approved