An Improvement on Ranks of Explicit Tensors
Discrete Mathematics
2011-02-11 v2 Computational Complexity
Abstract
We give constructions of n^k x n^k x n tensors of rank at least 2n^k - O(n^(k-1)). As a corollary we obtain an [n]^r shaped tensor with rank at least 2n^(r/2) - O(n^(r/2)-1) when r is odd. The tensors are constructed from a simple recursive pattern, and the lower bounds are proven using a partitioning theorem developed by Brockett and Dobkin. These two bounds are improvements over the previous best-known explicit tensors that had ranks n^k and n^(r/2) respectively
Keywords
Cite
@article{arxiv.1102.0580,
title = {An Improvement on Ranks of Explicit Tensors},
author = {Benjamin Weitz},
journal= {arXiv preprint arXiv:1102.0580},
year = {2011}
}