Tropical-basis conjecture for minors of a generic matrix
Tropical-basis conjecture. The (r+1)×(r+1)(r+1)\times(r+1)(r+1)×(r+1) minors of a d×nd\times nd×n matrix of variables are a tropical basis if and only if r≤2r\leq 2r≤2 or r≥min(d,n)−2r\geq \operatorname{min}(d,n)-2r≥min(d,n)−2.
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