2 problems

Let $\omega\in S_n$ be a permutation. An $\omega$-chamber weakly separated collection is a collection of subsets of $\{1,2,\ldots,n\}$ in the sense introduced by Leclerc and Zelevi…

Let $[n]=\{1,\ldots,n\}$, and let $2^{[n]}$ be its Boolean cube. A collection $C\subseteq 2^{[n]}$ is weakly separated when every two members are weakly separated in the sense of L…