3 problems

Let $W=B_n$ be generated by $S=\{s_1,\ldots,s_n\}$, with the usual labeling in which $s_{n-1}s_n$ has order $4$, and let $J=S\setminus\{s_k\}$. For the displayed reduced words, def…

Let $(W,S)$ be a finite Coxeter group, let $\boldsymbol{\operatorname{Sort}}_\omega(W)$ be a distributive sorting order, and let $J=S\setminus\{s\}$ for some $s\in S$. Write $W_J$…

A distributive sorting order is a sorting order that is a distributive lattice, and types $B$, $C$, and $D$ refer to the corresponding finite Coxeter types. Completeness conjecture…