On matrices with different tropical and Kapranov ranks
Combinatorics
2012-07-20 v1
Abstract
In this note, we generalize the technique developed in [13] and prove that every 5xn matrix of tropical rank at most 3 has Kapranov rank at most 3, for the ground field that contains at least 4 elements. For the ground field either F_2 or F_3, we construct an example of a 5x5 matrix with tropical rank 3 and Kapranov rank 4.
Keywords
Cite
@article{arxiv.1207.4697,
title = {On matrices with different tropical and Kapranov ranks},
author = {Yaroslav Shitov},
journal= {arXiv preprint arXiv:1207.4697},
year = {2012}
}