Kapranov rank vs. tropical rank-Reference-Cited by-同舟云学术

Kapranov rank vs. tropical rank

Published:2006-02-08 Issue:9 Volume:134 Page:2487-2494
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Kim K.,Roush F.

Abstract

We show that determining Kapranov rank of tropical matrices is not only NP-hard over any infinite field, but if solving Diophantine equations over the rational numbers is undecidable, then determining Kapranov rank over the rational numbers is also 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2006-134-09/S0002-9939-06-08426-7/S0002-9939-06-08426-7.pdf

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4. M. Develin, F. Santos, and B. Sturmfels, On the rank of a tropical matrix, arxiv:math.CO/0312114.

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