English

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.

Keywords

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

R2 v1 2026-07-22T16:46:56.993Z