Bijections for refined restricted permutations

2002/12/23 by Sergi Elizalde, Elizalde, Sergi, Igor Pak +1
Computer Science · Mathematics · #05A05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05

paper · pdf · doi:10.48550/arxiv.math/0212328

9 pages, 4 figures

arxiv created 2002/12/23 · openalex publication_date 2002/12/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a bijection between 321- and 132-avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of recent results of Robertson, Saracino and Zeilberger, and the first author. We also show that our bijection preserves additional statistics, which extends the previous results.

Citations

• On the diagram of 132-avoiding permutations

Related

• Classification of bijections between 321- and 132-avoiding permutations
• Fixed points and excedances in restricted permutations
• A bijection between 321- and 213-avoiding permutations preserving t-stack-sortability
• On Two Bijections from S_n(321) to S_n(132)
• Combinatorial of restricted permutations according to the number of crossings