2 problems

Let ${\mathcal{P}}(m,n)$ be the partial permutohedron, and let $k$ be a nonnegative integer. Heuer and Striker proved that, for any $m$ and $k$, the faces of ${\mathcal{P}}(m,m)$ o…

Let $\mathcal{P}(m,n)$ be the partial permutohedron and let $\mathcal{B}_m$ be the Boolean lattice of subsets of $[m]$. For a chain in $\mathcal{B}_m$, the difference between its l…