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arXiv · 2610.02756

Motzkin Numbers Count 2-Stack-Sortable Permutations Ending in Their Least Entry

Ryota Inagaki·Michael Luo
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Abstract

We prove the following conjecture of Zhang (arXiv:2604.10779, Conjecture 6.1): for $n \geq 0$, the number of $2$-stack-sortable permutations of $\{0,1,\dots,n\}$ ending in $0$ is the $n$th Motzkin number. By Zhang's result, there is a bijection between $2$-stack-sortable permutations ending in their least element and standard composition tableaux of width at most $2$. We then show bijectively that there are an equal number of these and standard Young tableaux of width at most $3$, which are known to be counted by the Motzkin numbers.

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Ryota Inagaki, Michael Luo. 2026-10-02. Motzkin Numbers Count 2-Stack-Sortable Permutations Ending in Their Least Entry. https://arxiv.org/abs/2610.02756

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