A sefl-dual poset on objects counted by the Catalan numbers
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 $P$.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- November 1998
- DOI:
- 10.48550/arXiv.math/9811067
- arXiv:
- arXiv:math/9811067
- Bibcode:
- 1998math.....11067B
- Keywords:
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- Combinatorics;
- 05A18;
- 06A07
- E-Print:
- 6 pages, 1 Figure