Sergi Elizalde - Continued fractions for permutation statistics

dmtcs:3225 - Discrete Mathematics & Theoretical Computer Science, June 25, 2018, Vol. 19 no. 2, Permutation Patterns 2016 -
Continued fractions for permutation statisticsArticle

Authors: Sergi Elizalde

    We explore a bijection between permutations and colored Motzkin paths that has been used in different forms by Foata and Zeilberger, Biane, and Corteel. By giving a visual representation of this bijection in terms of so-called cycle diagrams, we find simple translations of some statistics on permutations (and subsets of permutations) into statistics on colored Motzkin paths, which are amenable to the use of continued fractions. We obtain new enumeration formulas for subsets of permutations with respect to fixed points, excedances, double excedances, cycles, and inversions. In particular, we prove that cyclic permutations whose excedances are increasing are counted by the Bell numbers.

    Volume: Vol. 19 no. 2, Permutation Patterns 2016
    Section: Permutation Patterns
    Published on: June 25, 2018
    Accepted on: June 18, 2018
    Submitted on: August 1, 2017
    Keywords: Mathematics - Combinatorics,05A05 (Primary) 05A15, 05A19, 30B70, 05A18 (Secondary)
      Source : OpenAIRE Graph
    • Pattern avoidance in dynamical systems; Funder: National Science Foundation; Code: 1001046

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