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A sefl-dual poset on objects counted by the Catalan numbers

Miklos Bona
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Abstract

We examine the poset $P$ of 132-avoiding $n$-permutations ordered by descents. We show that this poset is the "coarsening" of the well-studied poset $Q$ of noncrossing partitions . In other words, if $x<y$ in $Q$, then $f(y)<f(x)$ in $P$, where $f$ is the canonical bijection from the set of noncrossing partitions onto that of 132-avoiding permutations. This enables us to prove many properties of $P$.

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Miklos Bona. 1998-11-10. A sefl-dual poset on objects counted by the Catalan numbers. https://arxiv.org/abs/math/9811067

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