To appear in Proceedings of the American Mathematical Society, 2006 ?
Dominique Foata, Guo-Niu Han
SIGNED WORDS AND PERMUTATIONS, I; A FUNDAMENTAL TRANSFORMATION
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.
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