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arxiv: 1209.1664 · v2 · pith:6JYV236Znew · submitted 2012-09-07 · 💻 cs.CC · math.AG

Explicit tensors of border rank at least 2n-1

classification 💻 cs.CC math.AG
keywords ranktensorsborderequalequationsotimesshowingalexeev
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For odd n, I write down tensors in C^n\otimes C^n\otimes C^n of border rank 2n-1, showing the non-triviality of the Young-flattening equations of Landsberg-Ottaviani. I also study the border rank of the tensors of Alexeev et. al., showing the tensors their tensors T_{2^k}, despite having rank equal to 2^{k+1}-1, have border rank equal to 2^k, the minimum of any concise tensor. I also study the equations of Griesser.

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