  For the ordered set $[n]$ of $n$ elements, we consider the class $\Bscr_n$ of
bases $B$ of tropical Pl\"ucker functions on $2^{[n]}$ such that $B$ can be
obtained by a series of mutations (flips) from the basis formed by the
intervals in $[n]$. We show that these bases are representable by special
wiring diagrams and by certain arrangements generalizing rhombus tilings on the
$n$-zonogon. Based on the generalized tiling representation, we then prove that
each weakly separated set-system in $2^{[n]}$ having maximum possible size
belongs to $\Bscr_n$, thus answering affirmatively a conjecture due to Leclerc
and Zelevinsky. We also prove an analogous result for a hyper-simplex
$\Delta_n^m=\{S\subseteq[n]\colon |S|=m\}$.
