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Periodic Points of Consecutive-Pattern-Avoiding Stack-Sorting Maps (2308.05868v1)
Published 10 Aug 2023 in math.CO and math.DS
Abstract: West's stack-sorting map involves a stack which avoids the permutation $21$ consecutively. Defant and Zheng extended this to a consecutive-pattern-avoiding stack-sorting map $SC_\sigma$, where the stack must always avoid a given permutation $\sigma$ consecutively. We address one of the main conjectures raised by Defant and Zheng in their dynamical approach to $SC_\sigma$. Specifically, we show that the periodic points of $SC_\sigma$ are precisely the permutations that consecutively avoid $\sigma$ and its reverse.