  We discuss arrangements of equal minors of totally positive matrices. More
precisely, we investigate the structure of equalities and inequalities between
the minors. We show that arrangements of equal minors of largest value are in
bijection with sorted sets, which earlier appeared in the context of alcoved
polytopes and Gr\"obner bases. Maximal arrangements of this form correspond to
simplices of the alcoved triangulation of the hypersimplex; and the number of
such arrangements equals the Eulerian number. On the other hand, we prove in
many cases that arrangements of equal minors of smallest value are exactly
weakly separated sets. Weakly separated sets, originally introduced by Leclerc
and Zelevinsky, are closely related to the positive Grassmannian and the
associated cluster algebra. However, we also construct examples of arrangements
of smallest minors which are not weakly separated using chain reactions of
mutations of plabic graphs.
