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arXiv · 1908.08896

A bound for the Waring rank of the determinant via syzygies

Mats Boij·Zach Teitler
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Abstract

We show that the Waring rank of the $3 \times 3$ determinant, previously known to be between $14$ and $18$, is at least $15$. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the cactus rank of the $3 \times 3$ permanent is at least $14$.

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Mats Boij, Zach Teitler. 2019-11-08. A bound for the Waring rank of the determinant via syzygies. https://arxiv.org/abs/1908.08896

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