Two oiseau decompositions of permutations and their application to Eulerian calculus

  • Authors:

  • Dominique Foata;Arthur Randrianarivony

  • Affiliations:

  • Institut Lothaire, Strasbourg, France;Faculté des Sciences, Université d'Antananarivo, Antananarivo, Madagascar

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2006

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Abstract

Two transformations are constructed that map the permutation group onto a well-defined subset of a partially commutative monoid generated by the so-called oiseaux. Those transformations are then used to show that some bivariable statistics introduced by Babson and Steingrímsson are Euler-Mahonian.