To appear in Proceedings of the American Mathematical Society, 2006 ? (10 pages)

Dominique Foata, Guo-Niu Han

SIGNED WORDS AND PERMUTATIONS, I; A FUNDAMENTAL TRANSFORMATION

Abstract. The statistics major index and inversion number, usually defined on ordinary words, have their counterparts in signed words, namely the so-called flag-major index and flag-inversion number. We give the construction of a new transformation on those signed words that maps the former statistic onto the latter one. It is proved that the transformation also preserves two other set-statistics: the inverse ligne of route and the lower records.

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

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