On bijections between 231-avoiding permutations and Dyck paths

2008/03/26 by Christian Stump, Stump, Christian
Mathematics · #05A05 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0803.3706

openalex publication_date 2008/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a bijection between 231-avoiding permutations and Dyck paths that sends the sum of the major index and the inverse major index of a 231-avoiding permutation to the major index of the corresponding Dyck path. Furthermore, we relate this bijection to others and exhibit a bistatistic on 231-avoiding permutations which is related to the q,t-Catalan numbers.

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