2 problems

Let $n\geq 1$ and let $\sigma\in\mathfrak{S}_{n+1}$. Let $R_{\bullet}(\sigma)$ denote the set of one-element commutation classes of reduced words of $\sigma$. The possible-cardinal…

Let $n\geq 1$ and let $\sigma\in\mathfrak{S}_{n+1}$. Write $R(\sigma)$ for the set of reduced words of $\sigma$ and $C(\sigma)$ for the set of commutation classes of reduced words.…