  For a permutation $\omega\in S_n$, Leclerc and Zelevinsky \cite{LZ}
introduced a concept of $\omega$-{\em chamber weakly separated collection} of
subsets of $\{1,2,...,n\}$ and conjectured that all inclusion-wise maximal
collections of this sort have the same cardinality $\ell(\omega)+n+1$, where
$\ell(\omega)$ is the length of $\omega$. We answer affirmatively this
conjecture and present a generalization and additional results.
