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A bound for the Waring rank of the determinant via syzygies

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 نشر من قبل Zach Teitler
 تاريخ النشر 2019
  مجال البحث
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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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