A284308 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.
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, 1621, 6, 1, 1, 5040, 2882071, 23096640, 2940841, 11256, 7, 1, 1, 40320, 260415373, 18754813440, 14346274601, 180296088, 79717, 8, 1, 1, 362880, 31088448777, 24874143759360, 153480509680141, 9859397817600, 11559133741, 572928, 9, 1
Offset: 1
Examples
Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, ... 1, 2, 6, 24, 120, 720, ... 1, 3, 37, 997, 44121, 2882071, ... 1, 4, 240, 51264, 23096640, 18754813440, ... 1, 5, 1621, 2940841, 14346274601, 153480509680141, ... 1, 6, 11256, 180296088, 9859397817600, 1435747717722810960, ...
Links
- Alois P. Heinz, Antidiagonals n = 1..18, flattened
- Shalosh B. Ekhad and Doron Zeilberger, On the Number of Singular Vector Tuples of Hyper-Cubical Tensors, 2016; also arXiv preprint arXiv:1605.00172, 2016.
- Shmuel Friedland and Giorgio Ottaviani, The number of singular vector tuples and uniqueness of best rank-one approximation of tensors, Found. Comput. Math. 14 (2014), no. 6, 1209-1242.
- Bernd Sturmfels, Tensors and Their Eigenvalues, Notices AMS, 63 (No. 6, 2016), 606-606.