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arXiv · 2604.10779

Polynomial Time Enumeration of t-Stack-Sortable Permutations Ending in Their Least Entry

Jerry Zhang
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Abstract

We study the behavior of West's stack-sorting map $s$ on permutations whose last entry is also their least. Let $S_{n}':=\{\pi0\mid \pi\in S_n\}$ where $\pi0$ denotes the concatenation of $\pi$ and $0$. For each permutation $\pi\in S_n'$, we introduce a new combinatorial object known as the stack-sorting tableau $T_{\pi}$, which ultimately serves as the key ingredient in the first polynomial time algorithm for counting the number of $t$-stack-sortable permutations in $S_n'$. We then establish a precise relationship between the behavior of $s$ on $S_{n}'$ and on $S_{n}$.

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Jerry Zhang. 2026-04-12. Polynomial Time Enumeration of t-Stack-Sortable Permutations Ending in Their Least Entry. https://arxiv.org/abs/2604.10779

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