Explicit tensors of border rank at least 2n-1
Computational Complexity
2013-08-08 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1209.1664,
title = {Explicit tensors of border rank at least 2n-1},
author = {J. M. Landsberg},
journal= {arXiv preprint arXiv:1209.1664},
year = {2013}
}
Comments
8 pages, version 2 contains a study of Griesser's equations