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2-stack sortable permutations with a given number of runs

Miklós Bóna
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Abstract

Using earlier results we prove a formula for the number $W_{(n,k)}$ of 2-stack sortable permutations of length $n$ with $k$ runs, or in other words, $k-1$ descents. This formula will yield the suprising fact that there are as many 2-stack sortable permutations with $k-1$ descents as with $k-1$ ascents. We also prove that $W_{(n,k)}$ is unimodal in $k$, for any fixed $n$.

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Miklós Bóna. 1997-05-16. 2-stack sortable permutations with a given number of runs. https://arxiv.org/abs/math/9705220

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