# A counterexample to Comon's conjecture

## TL;DR

This paper provides a specific counterexample to Comon's conjecture by demonstrating a symmetric tensor that cannot be decomposed into symmetric simple tensors despite having a symmetric rank.

## Contribution

The authors construct the first explicit counterexample to Comon's conjecture for a large symmetric tensor, challenging the assumption that symmetric and non-symmetric tensor ranks always coincide.

## Key findings

- Counterexample tensor size: 800x800x800
- Tensor decomposed into 903 simple tensors
- Cannot be decomposed into 903 symmetric simple tensors

## 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.