On the diagram of 132-avoiding permutations

2002/08/01 by Astrid Reifegerste, Reifegerste, Astrid · 2 citations
Mathematics · #05A05 #05A15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A15

paper · pdf · doi:10.48550/arxiv.math/0208006

20 pages; additional reference is added

openalex publication_date 2002/08/01 · arxiv created 2002/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Flags, Schubert polynomials, degeneracy loci, and determinantal formulas

Cited by

• A bijection between 321- and 213-avoiding permutations preserving t-stack-sortability
• An application of a bijection of Mansour, Deng, and Du

Related

• Permutations with restricted patterns and Dyck paths
• On the diagram of Schroeder permutations
• An application of a bijection of Mansour, Deng, and Du
• Combinatorial bijections from hatted avoiding permutations in S_n(132) to generalized Dyck and Motzkin paths
• Permutations Containing and Avoiding 123 and 132 Patterns