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West's stack-sorting map involves a stack which avoids the permutation $21$consecutively. Defant and Zheng extended this to a consecutive-pattern-avoidingstack-sorting map $SC_\sigma$, where the stack must always avoid a givenpermutation $\sigma$ consecutively. We address one of the main conjecturesraised by Defant and Zheng in their dynamical approach to $SC_\sigma$.Specifically, we show that the periodic points of $SC_\sigma$ are precisely thepermutations that consecutively avoid $\sigma$ and its reverse.

Periodic Points of Consecutive-Pattern-Avoiding Stack-Sorting Maps