Accepted for publication in Electronic J. Combinatorics (18 pages)

Dominique Foata, Guo-Niu Han

SIGNED WORDS AND PERMUTATIONS, II; THE EULER-MAHONIAN POLYNOMIALS

Abstract. As for the symmetric group of ordinary permutations there is also a statistical study of the group of signed permutations, that consists of calculating multivariable generating functions for this group by statistics involving record values and the length function. Two approaches are here systematically explored, using the flag-major index on the one hand, and the flag-inversion number on the other hand. The MacMahon Verfahren appears as a powerful tool throughout.

foata at math.u-strasbg.fr, guoniu at math.u-strasbg.fr

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