4 problems

Nearly symmetric word conjecture. A word has positive trace for every pair of positive definite letters if and only if the word is nearly symmetric.

Let $\operatorname{FIM}_1$ be the free inverse monoid of rank $1$. Write $\operatorname{WP}(\operatorname{FIM}_1)$ and $\iota(\operatorname{FIM}_1)$ for its two word problem langua…

Let $(\mathcal{S},\mathcal{R})$ be an Artin–Tits presentation, and let denote the reducing equivalence defined earlier in the paper. Reducing conjecture. Every Artin–Tits presentat…

Let $B_n$ be the braid group with generating set $\Sigma=\{\sigma_1,\ldots,\sigma_{n-1}\}$, and let $l_\Sigma(w)$ denote the $\Sigma$-length of a braid $w$. A braid word is…