Kapranov rank vs. tropical rank |
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| Authors: | K H Kim F W Roush |
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| Institution: | Department of Mathematics, Alabama State University, Montgomery, Alabama 36101-0271 -- and -- Fellow, Korean Academy of Science and Technology ; Department of Mathematics, Alabama State University, Montgomery, Alabama 36101-0271 |
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| 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. |
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| Keywords: | Kapranov rank tropical rank |
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