2 problems

Let $\mathfrak{S}_3$ denote the symmetric group on three letters, let $\Pi\subseteq\mathfrak{S}_3$, and let $B_n(\Pi)$ be the associated polytope. A conjecture on the integer decom…

Let $P_n(132,213)$ be the pattern-avoiding polytope associated with the patterns $132$ and $213$. A cube conjecture asserts that, for every $n$, $P_n(132,213)$ is a combinatorial c…