|
%I #11 Oct 18 2018 15:54:26
%S 1,1,1,1,2,1,1,6,3,1,1,24,37,4,1,1,120,997,240,5,1,1,720,44121,51264,
%T 1621,6,1,1,5040,2882071,23096640,2940841,11256,7,1,1,40320,260415373,
%U 18754813440,14346274601,180296088,79717,8,1,1,362880,31088448777,24874143759360,153480509680141,9859397817600,11559133741,572928,9,1
%N Number A(n,k) of singular vector tuples for a general k-dimensional {n}^k tensor; square array A(n,k), n>=1, k>=1, read by antidiagonals.
%H Alois P. Heinz, <a href="/A284308/b284308.txt">Antidiagonals n = 1..18, flattened</a>
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/svt.html">On the Number of Singular Vector Tuples of Hyper-Cubical Tensors</a>, 2016; also arXiv preprint arXiv:1605.00172, 2016.
%H Shmuel Friedland and Giorgio Ottaviani, <a href="http://dx.doi.org/10.1007/s10208-014-9194-z">The number of singular vector tuples and uniqueness of best rank-one approximation of tensors</a>, Found. Comput. Math. 14 (2014), no. 6, 1209-1242.
%H Bernd Sturmfels, <a href="http://www.ams.org/publications/journals/notices/201606/rnoti-p604.pdf">Tensors and Their Eigenvalues</a>, Notices AMS, 63 (No. 6, 2016), 606-606.
%e Square array A(n,k) begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 6, 24, 120, 720, ...
%e 1, 3, 37, 997, 44121, 2882071, ...
%e 1, 4, 240, 51264, 23096640, 18754813440, ...
%e 1, 5, 1621, 2940841, 14346274601, 153480509680141, ...
%e 1, 6, 11256, 180296088, 9859397817600, 1435747717722810960, ...
%Y Columns k=1-9 give: A000012, A000027, A271905, A272551, A283829, A283830, A287083, A287084, A287085.
%Y Rows n=1-3 give: A000012, A000142, A274308.
%Y Main diagonal gives A284309.
%K nonn,tabl
%O 1,5
%A _Alois P. Heinz_, Mar 24 2017
|
