A sefldual poset on objects counted by the Catalan numbers
Abstract
We examine the poset $P$ of 132avoiding $n$permutations ordered by descents. We show that this poset is the "coarsening" of the wellstudied 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 132avoiding permutations. This enables us to prove many properties of $P$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.math/9811067
 arXiv:
 arXiv:math/9811067
 Bibcode:
 1998math.....11067B
 Keywords:

 Combinatorics;
 05A18;
 06A07
 EPrint:
 6 pages, 1 Figure