##### to appear in Monatshefte für Mathematik

# Dominique Foata, Guo-Niu Han

#
FIX-MAHONIAN CALCULUS, III: A QUADRUPLE DISTRIBUTION

**Abstract.**
A four-variable distritution on permutations is derived, with two dual
combinatorial interpretations. The first one includes the number of fixed points
"fix", the second the so-called "pix" statistic. This shows that the duality
between derangements and desarrangements can be extended to the case of
multivariable statistics. Several specializations are obtained, including the
joint distribution of (des,exc), where "des" and "exc" stand for the number of
descents and excedances, respectively.

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

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