  We introduce a new technique to study pattern avoidance in dynamical systems,
namely the use of a commuter function between non-conjugate dynamical systems.
We investigate the properties of such a commuter function, specifically $h :
[0,1] \to [0,1]$ satisfying $T_1 \circ h = h \circ T_\mu$, where $T_\mu$
denotes a symmetric tent map of height $\mu$. We make use of this commuter
function to prove strict inclusion of the set of allowed patterns of $T_\mu$ in
the set of allowed patterns of $T_1$.
