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arXiv · 2410.17057

Stack-sorting with Stacks Avoiding Vincular Patterns

William Zhao
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Abstract

We introduce the stack-sorting map $\text{SC}_σ$ that sorts, in a right-greedy manner, an input permutation through a stack that avoids some vincular pattern $σ$. The stack-sorting maps of Cerbai et al. in which the stack avoids a pattern classically and Defant and Zheng in which the stack avoids a pattern consecutively follow as special cases. We first characterize and enumerate the sorting class $\text{Sort}(\text{SC}_σ)$, the set of permutations sorted by $s\circ\text{SC}_σ$, for seven length $3$ patterns $σ$. We also decide when $\text{Sort}(\text{SC}_σ)$ is a permutation class. Next, we compute $\max_{π\in \mathfrak S_n}|\text{SC}_σ^{-1}(π)|$ and characterize the periodic points of $\text{SC}_σ$ for several length $3$ patterns $σ$. We end with several conjectures and open problems.

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William Zhao. 2024-10-19. Stack-sorting with Stacks Avoiding Vincular Patterns. https://arxiv.org/abs/2410.17057

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