Subgroups of $S{L}_2(\mathbb{Z})$ characterized by certain continued fraction representations

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

For positive integers $u$ and $v$, let $L_u=\left[\begin{array}{cc}1& 0\\ u& 1\end{array}\right]$ and $R_v=\left[\begin{array}{cc}1& v\\ 0& 1\end{array}\right]$. Let $S_{u,v}$ be the monoid genera…