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Mixed subdivisions and ranks of tropical matrices


Author: Yaroslav Shitov
Journal: Proc. Amer. Math. Soc. 142 (2014), 15-19
MSC (2010): Primary 15A03, 15A80
DOI: https://doi.org/10.1090/S0002-9939-2013-11766-1
Published electronically: September 6, 2013
MathSciNet review: 3119176
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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.


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Additional Information

Yaroslav Shitov
Affiliation: Moscow State University, Leninskie Gory, 119991, GSP-1, Moscow, Russia
Address at time of publication: National Research University – Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow, 101000, Russia
Email: yaroslav-shitov@yandex.ru

DOI: https://doi.org/10.1090/S0002-9939-2013-11766-1
Keywords: Tropical semiring, matrix theory, Barvinok rank, Kapranov rank.
Received by editor(s): October 3, 2011
Received by editor(s) in revised form: February 22, 2012
Published electronically: September 6, 2013
Communicated by: Jim Haglund
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.