A counterexample to Comon's conjecture

Abstract

We present an example of a symmetric tensor of size $800\times 800\times 800$ which can be written a sum of $903$ simple tensors with complex entries but not as a sum of $903$ symmetric simple tensors.

arXiv comment13 pages; the same example as in ver. 1; section 4 corrected; section 2 split into two; more details added