Kapranov rank vs. tropical rank

Details Kapranov rank vs. tropical rank Kapranov rank vs. tropical rank

2005-03-02

arxiv.org/abs/math/0503044v2

Mathematics

Combinatorics

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

Scientific paper

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.

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