Kapranov rank vs. tropical rank

被引：17
|
作者：
Kim, KH [1 ]
Roush, FW [1 ]
机构：
[1] Alabama State Univ, Dept Math, Montgomery, AL 36101 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 09期
关键词：
Kapranov rank; tropical rank;
D O I：
10.1090/S0002-9939-06-08426-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：2487 / 2494
页数：8
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