Inversion polynomials for 321-avoiding permutations

2011/12/27 by Szu-En Cheng, Sergi Elizalde, Cheng, Szu-En +5 · 1 citation
Computer Science · Mathematics · #05A05 (Primary) 05A10 #05A15 #05A19 #05A30 #11A07 #11A55 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1112.6014

openalex publication_date 2011/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formulas for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin paths, polyominoes, and continued fractions.

Citations

• Wilf Equivalence for the Charge Statistic

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• Inversion polynomials for 321-avoiding permutations: addendum

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