Words have bounded width in $\operatorname{SL}(n, \mathbb{Z})$. (July 2019) - Avni, Nir; Meiri, Chen
Abstract : We prove two results about the width of words in $\operatorname{SL}_{n}(\mathbb{Z})$ . The first is that, for every $n\geqslant 3$, there is a constant $C(n)$ such that the width of any word in $\operatorname{SL}_{n}(\mathbb{Z})$ is less than $C(n)$ . The second result is that, for any word $w$, if $n$ is big enough, the width of $w$ in $\operatorname{SL}_{n}(\mathbb{Z})$ is at most 87.