On the diagram of 132-avoiding permutations

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.

20 pages; additional reference is added

References in corpus (2)

• Restricted permutations and Chebyshev polynomials
• The excedances and descents of bi-increasing permutations

Cited by in corpus (6)

• Bijections for refined restricted permutations
• A simple and unusual bijection for Dyck paths and its consequences
• A generalization of the Simion-Schmidt bijection for restricted permutations
• On the diagram of Schroeder permutations
• An application of a bijection of Mansour, Deng, and Du
• Multiple pattern avoidance with respect to fixed points and excedances