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On the diagram of 132-avoiding permutations

Astrid Reifegerste
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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.

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Astrid Reifegerste. 2002-10-15. On the diagram of 132-avoiding permutations. https://arxiv.org/abs/math/0208006

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