Words have bounded width in
Nir Avni, Chen Meiri · Compositio Mathematica · 2019
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.