Kapranov rank vs. tropical rank
Combinatorics
2007-05-23 v2
Abstract
We show that determining Kapranov rank of tropical matrices is not only NP-hard over any infinite field but also if solving Diophantine equations over the rational numbers is undecidable, then determining Kapranov rank over the rational numbers is undecidable. We prove that Kapranov rank of tropical matrices is not bounded in terms of tropical rank, answering a question of Develin, Santos, and Sturmfels.
Keywords
Cite
@article{arxiv.math/0503044,
title = {Kapranov rank vs. tropical rank},
author = {K. H. Kim and F. W. Roush},
journal= {arXiv preprint arXiv:math/0503044},
year = {2007}
}
Comments
Replacement is to fill a gap in the proof of Theorem 3.1