On universal quadratic inequalities for minors of TNN matrices

Abstract

For positive integers $n,n^{\prime }$, we give a combinatorial characterization for the set of quadratic inequalities on minors that are valid for all $n\times n^{\prime }$ 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 Lindström's construction.

14 pages, 8 figures. Compared with the initial version, introduction and additional illustrations to the theorem are added