##### Europ. J. Combinatorics, vol. 27, 2006, p. 342-363.

# Dominique Foata, Arthur Randrianarivony

# Two Oiseau Decompositions of Permutations and their
Application to Eulerian Calculus

**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 trans formations are then used to show
that some bivariable statistics introduced by Babson and
Steingrimsson are Euler-Mahonian

foata at math dot u-strasbg dot fr,
arthur at univ-antananarivo dot mg

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