On the construction of a counterexample to Strassen's rank additivity conjecture
Algebraic Geometry
2025-07-25 v1
Abstract
The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individual ranks. In the last decades, this conjecture has been a central topic in tensor rank theory and its implications for computational complexity. In 2019, Yaroslav Shitov disproved this conjecture in its general form by showing the existence of a counter-example using a dimension counting argument. In this paper, we provide an overview of the Strassen problem and Shitov's work and revisit his counterexample with a detailed explanation, offering an alternative proof.
Cite
@article{arxiv.2507.17890,
title = {On the construction of a counterexample to Strassen's rank additivity conjecture},
author = {Viktoriia Borovik and Cosimo Flavi and Paweł Pielasa and Anatoli Shatsila and Jeyoung Song},
journal= {arXiv preprint arXiv:2507.17890},
year = {2025}
}
Comments
37 pages, 9 figures