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MiS Preprint

Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in $\mathbb{C}^m\otimes \mathbb{C}^m\otimes \mathbb{C}^m$

Joseph Landsberg and Mateusz Michałek


We write down an explicit sequence of tensors in $\mathbb{C}^m\otimes\mathbb{C}^m\otimes\mathbb{C}^m$, for all m sufficiently large, having border rank at least 2.02m, overcoming a longstanding barrier. We obtain our lower bounds via the border substitution method.

MSC Codes:
15A69, 14L35, 68Q15

Related publications

2019 Repository Open Access
Joseph M. Landsberg and Mateusz Michałek

Towards finding hay in a haystack : explicit tensors of border rank greater than \(2.02m\) in \(C^{m}\otimes C^{m}\otimes C^{m}\)