Mixed subdivisions and ranks of tropical matrices
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- by Yaroslav Shitov
- Proc. Amer. Math. Soc. 142 (2014), 15-19
- DOI: https://doi.org/10.1090/S0002-9939-2013-11766-1
- Published electronically: September 6, 2013
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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.References
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Bibliographic 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
- MR Author ID: 864960
- Email: yaroslav-shitov@yandex.ru
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3119176