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On the diagram of 132-avoiding permutations

by Reifegerste, A..

Series: 2002-26, Preprints

05A05 Permutations, words, matrices
05A15 Exact enumeration problems, generating functions

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.

132-avoiding permutation, 321-avoiding permutation, diagram of a permutation, partition, Young diagram, Dyck path, permutation pattern