Explicit tensors of border rank at least 2n-1

Abstract

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.