On the diagram of 132-avoiding permutations

Authors:
Astrid Reifegerste
Affiliations:
Institut für Mathematik, Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
Venue:
European Journal of Combinatorics
Year:
2003

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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.