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We introduce a new technique  study pattern avoidance in dynamical systems, namely, the use of a commuter function between nonconjugate 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  prove strict inclusion of the set of allowed patterns of $T_mu$ in the set of allowed patterns of $T_1$.

Allowed Patterns of Symmetric Tent Maps via Commuter Functions