2-stack sortable permutations with a given number of runs

Details 2-stack sortable permutations with a given number of runs 2-stack sortable permutations with a given number of runs

1997-05-16

arxiv.org/abs/math/9705220v1

Mathematics

Combinatorics

Scientific paper

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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