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Bijections for Rota–Baxter words and Schröder paths

Volume 153 / 2018

Nancy S. S. Gu, Li-Jun Hao Colloquium Mathematicum 153 (2018), 103-119 MSC: Primary 05A15; Secondary 08B20. DOI: 10.4064/cm7142-6-2017 Published online: 16 April 2018

Abstract

Rota–Baxter words were first introduced by Ebrahimi-Fard and Guo as canonical bases of free Rota–Baxter algebras. In this paper, we find that the Rota–Baxter words $R(n,n)$ with one idempotent generator and one idempotent operator are counted by the Catalan number. Then we construct some bijections between Rota–Baxter words and Schröder paths. In particular, we consider enumeration and generating functions of bracketed Rota–Baxter words and Rota–Baxter words whose right brackets are behind the rightmost left bracket, by using the Schröder paths viewpoint.

Authors

  • Nancy S. S. GuCenter for Combinatorics
    LPMC
    Nankai University
    300071 Tianjin, P.R. China
    e-mail
  • Li-Jun HaoCenter for Combinatorics
    LPMC
    Nankai University
    300071 Tianjin, P.R. China
    e-mail

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