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Article

When do the r-by-r minors of a matrix form a tropical basis?

Journal of Combinatorial Theory, Series A. 2013. Vol. 120. No. 6. P. 1166-1201.

We show that the r-by-r minors of a d-by-n matrix of variables form a tropical basis of the ideal they generate if and only if one of the following conditions holds: (i) r⩽3, (ii) r=min{d,n}, (iii) r=4 and min{d,n}⩽6. This answers a question raised by M. Chan, A. Jensen, and E. Rubei.