English

A counterexample to Comon's conjecture

Combinatorics 2017-08-29 v2

Abstract

We present an example of a symmetric tensor of size 800×800×800800\times 800\times 800 which can be written a sum of 903903 simple tensors with complex entries but not as a sum of 903903 symmetric simple tensors.

Cite

@article{arxiv.1705.08740,
  title  = {A counterexample to Comon's conjecture},
  author = {Yaroslav Shitov},
  journal= {arXiv preprint arXiv:1705.08740},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T19:57:41.314Z