[seqfan] Re: Number of nXn (0,1)-matrices A with A^2 = J?
W. Edwin Clark
wclark at mail.usf.edu
Sun Mar 12 19:36:43 CET 2017
I just finished calculating the 9x9 case and confirm the value 1330560.
My method was to take the 6 matrices A1, A2, A3, A4, A5, A6 found by Knuth
which
are representatives of the 6 distinct orbits of 9 x 9 matrices A such that
A^2 = J under the action of the 9! permutation matrices acting by
conjugation.
I found for each Ai the size n_i of the stabilizer of Ai. The stabilizer
orders
are [n_1,n_2,n_3,n_4,n_5,n_6] = [6,2,1,1,2,2] this give the
cardinality of the union of all orbits:
sum(9!/n_i, i=1..6) = 1330560.
On Sun, Mar 12, 2017 at 2:15 PM, Richard J. Mathar <mathar at mpia-hd.mpg.de>
wrote:
> Concerning http://list.seqfan.eu/pipermail/seqfan/2017-March/017353.html :
>
> By brute force enumeration the result for the 9x9 case is now in A283627.
>
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