2 problems

Weak Bruhat lattice EKR conjecture. For all values of $1\le r\le \frac12{n\choose2}$, the set ${\mathscr B}_n(r)$ is EKR. Thus, for any $p\in{\mathscr B}_n(1)$,

For an $m$-element set $[m]$, let $\mathcal{S}_{[m],m}^*$ be the family of partial matchings represented by permutations of subsets of $[m]$, and let the $t$-star property mean tha…