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arXiv · 2308.05868

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

Ilaria Seidel·Nathan Sun
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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 $SC_σ$, where the stack must always avoid a given permutation $σ$ consecutively. We address one of the main conjectures raised by Defant and Zheng in their dynamical approach to $SC_σ$. Specifically, we show that the periodic points of $SC_σ$ are precisely the permutations that consecutively avoid $σ$ and its reverse.

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Ilaria Seidel, Nathan Sun. 2023-08-10. Periodic Points of Consecutive-Pattern-Avoiding Stack-Sorting Maps. https://arxiv.org/abs/2308.05868

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