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On universal quadratic inequalities for minors of TNN matrices

Published 4 Jun 2025 in math.CO | (2506.03754v1)

Abstract: In this note, for positive integers $n,n'$, we give a geometric-combinatorial characterization for the set of quadratic inequalities on minors that are valid for all $n\times n'$ totally nonnegative matrices. This is obtained as a consequence from our earlier results on ``stable'' quadratic identities on minors of matrices generated by flows in planar graphs via Lindstr\"om's construction.

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