Progress on the symmetric Strassen conjecture

TL;DR

This paper proves the symmetric Strassen conjecture for specific cases, demonstrating that the Waring rank is additive when certain conditions on the polynomials are met, advancing understanding in algebraic complexity.

Contribution

It establishes the additivity of Waring rank for the symmetric Strassen conjecture in new cases where one polynomial is a power, both have two variables, or one has small rank.

Findings

Waring rank is additive when either polynomial is a power.

Additivity holds for polynomials with two variables.

The conjecture is proved when either polynomial has small rank.

Abstract

Let F and G be homogeneous polynomials in disjoint sets of variables. We prove that the Waring rank is additive, thus proving the symmetric Strassen conjecture, when either F or G is a power, or F and G have two variables, or either F or G has small rank.