

A309258


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


7




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 DMS1852378 and DMS1560019.
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: A115647 A019437 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



