# On the strength of general polynomials

```@article{Bik2021OnTS,
title={On the strength of general polynomials},
author={Arthur Bik and A. Oneto},
journal={Linear and Multilinear Algebra},
year={2021}
}```
• Published 18 May 2020
• Mathematics
• Linear and Multilinear Algebra
A slice decomposition is an expression of a homogeneous polynomial as a sum of forms with a linear factor. A strength decomposition is an expression of a homogeneous polynomial as a sum of reducible forms. The slice rank and the strength of a polynomial are the minimal lengths of such decompositions, respectively. The slice rank is an upper bound for the strength and we observe that the gap between these two values can be arbitrary large. However, in line with a conjecture by Catalisano et al…
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The strength of a homogeneous polynomial (or form) \$f\$ is the smallest length of an additive decomposition expressing it whose summands are reducible forms. We show that the set of forms with bounded
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