  Fully commutative elements in types $B$ and $D$ are completely characterized
and counted by Stembridge. Recently, Feinberg-Kim-Lee-Oh have extended the
study of fully commutative elements from Coxeter groups to the complex setting,
giving an enumeration of such elements in $G(m,1,n)$. In this note, we prove a
connection between fully commutative elements in $B_n$ and in $G(m,1,n)$, which
allows us to characterize fully commutative elements in $G(m,1,n )$ by pattern
avoidance. Further, we present a counting formula for such elements in
$G(m,1,n)$.
