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A309258 a(n) is the number of distinct absolute values of determinants of order n Latin squares. 7

%I #31 Mar 19 2020 14:51:50

%S 1,1,1,3,6,197,3684,159561

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

%C 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.

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

%C a(9) >= 1747706. - _Hugo Pfoertner_, Nov 20 2019

%H Froylan Maldonado, <a href="/A309258/a309258.sage.txt">Code</a>

%H Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/data/latin.html">Latin squares</a>

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a309258.pdf">8X8 Latin squares: Illustration of occurrence counts of determinant values</a>, 5.7 MB, zoom in to see details (2019).

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a309258.zip">Occurrence counts of determinant values for n=1..8</a>, zipped (2019).

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

%o (Sage) # See Maldonado link.

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

%K nonn,hard,more

%O 1,4

%A _Alvaro R. Belmonte_, _Eugene Fiorini_, _Peterson Lenard_, _Froylan Maldonado_, _Sabrina Traver_, _Wing Hong Tony Wong_, Jul 19 2019

%E a(8) from _Hugo Pfoertner_, Aug 26 2019

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)