3 problems

Semi-convergence conjecture. Reduction is semi-convergent for every Artin–Tits monoid $M$.

For $n\geq 2$, let $B_n$ be the braid group with standard generators $\sigma_1,\ldots,\sigma_{n-1}$. For $e_1,\ldots,e_{n-1}\in\{1,-1\}$, let $\mathcal{HBM}(e_1,\ldots,e_{n-1})$ be…

For each $n$, let the $n$-low elements be the elements defined using the notion of $n$-small roots in the associated Coxeter group, and let the associated Artin--Tits monoid be the…