When do the r-by-r minors of a matrix form a tropical basis?
Combinatorics
2013-06-28 v1
Abstract
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 r<4, or r=min(d,n), or else r=4 and min(d,n)<7. This answers a question asked by M. Chan, A. Jensen, and E. Rubei.
Cite
@article{arxiv.1109.2240,
title = {When do the r-by-r minors of a matrix form a tropical basis?},
author = {Yaroslav Shitov},
journal= {arXiv preprint arXiv:1109.2240},
year = {2013}
}