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Words have bounded width in
$\operatorname{SL}(n,\mathbb{Z})$
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 7 / July 2019
- Published online by Cambridge University Press:
- 13 June 2019, pp. 1245-1258
- Print publication:
- July 2019
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- Article
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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.
