On the Chow-rank of the permanent

Rongyu Xu; Edinah Gnang

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arXiv · 2311.05890

On the Chow-rank of the permanent

Rongyu Xu·Edinah Gnang

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Abstract

We derive Glynn's formula from Ryser's formula for the permanent. We further establish via an orbital argument that Glynn's formula yields an optimal row-homogeneous Chow-decomposition of the permanent. We introduce a method for upper-bounding the Chow-rank of polynomials. Our method is based upon the Fundamental Theorem of Symmetric Polynomials. Finally we derive a parametric description of rank revealing row-homogeneous Chow-decompositions of the permanent. Our result provides an alternative approach to the parametrization first obtained by Glynn.

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Rongyu Xu, Edinah Gnang. 2023-11-10. On the Chow-rank of the permanent. https://arxiv.org/abs/2311.05890

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