Kapranov rank vs. tropical rank

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
Replacement is to fill a gap in the proof of Theorem 3.1

Keywords

Combinatorics, 15A99

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/74369

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503044
 http://arxiv.org/abs/math/0503044

Collections

arXiv