Maximal entries of elements in certain matrix monoids

Sandie Han, Ariane M. Masuda, Satyanand Singh +1

Let $L_u=\left[\begin{array}{cc}1& 0\\ u& 1\end{array}\right]$ and $R_v=\left[\begin{array}{cc}1& v\\ 0& 1\end{array}\right]$ be matrices in $S{L}_2(\mathbb{Z})$ with $u,v\ge 1$. Since the monoid generated…