On the diagram of 132-avoiding permutations
Combinatorics
2007-05-23 v3
Abstract
The diagram of a 132-avoiding permutation can easily be characterized: it is simply the diagram of a partition. Based on this fact, we present a new bijection between 132-avoiding and 321-avoiding permutations. We will show that this bijection translates the correspondences between these permutations and Dyck paths given by Krattenthaler and by Billey-Jockusch-Stanley, respectively, to each other. Moreover, the diagram approach yields simple proofs for some enumerative results concerning forbidden patterns in 132-avoiding permutations.
Cite
@article{arxiv.math/0208006,
title = {On the diagram of 132-avoiding permutations},
author = {Astrid Reifegerste},
journal= {arXiv preprint arXiv:math/0208006},
year = {2007}
}
Comments
20 pages; additional reference is added