Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2011, Number 5, Pages 58–61 (Mi vmumm723)  
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Example of the matrix of size $6\times6$ with different tropical rank and Kapranov rank

Ya. Shitov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (246 kB)
Abstract: We provide an example of a $6$-by-$6$ matrix $A$ such that $\operatorname{rk}_t(A)=4$, $\operatorname{rk}_K(A)=5$. This disproves the conjecture formulated by M. Chan, A. Jensen, and E. Rubei.
Key words: tropical semiring, tropical rank, Kapranov rank, tropical basis.
Received: 14.02.2011
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: Russian
Citation: Ya. Shitov, “Example of the matrix of size $6\times6$ with different tropical rank and Kapranov rank”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 5, 58–61
Citation in format AMSBIB
\Bibitem{Shi11}
\by Ya.~Shitov
\paper Example of the matrix of size $6\times6$ with different tropical rank and Kapranov rank
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2011
\issue 5
\pages 58--61
\mathnet{http://mi.mathnet.ru/vmumm723}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2964361}
\zmath{https://zbmath.org/?q=an:1304.15022}
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