Mixed subdivisions and ranks of tropical matrices

Shitov, Yaroslav

doi:10.1090/S0002-9939-2013-11766-1

Mixed subdivisions and ranks of tropical matrices
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Proc. Amer. Math. Soc. 142 (2014), 15-19 Request permission

Abstract:

We show that neither the Barvinok rank nor the Kapranov rank of a tropical matrix $M$ can be defined in terms of the regular mixed subdivision produced by $M$. This answers a question asked by Develin, Santos and Sturmfels.

References

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