On the number of Singular Vector Tuples of Hyper-Cubical Tensors

Doron Zeilberger, Shalosh B. XIV Ekhad

Publication date: 30 April 2016

Abstract: Shmuel Friedland and Giorgio Ottaviani's beautiful constant term expression for the number of singular vector tuples of generic tensors is used to derive a rational generating function for these numbers, that in turn, is used to obtain an asymptotic formula for the number of such tuples for n by n by n three-dimensional tensors, and to conjecture an asymptotic formula for the general d-dimensional case. A donation of 100 dollars, in honor of the first prover, will be made to the On-line Encyclopedia of Integer Sequences.

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