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

The following versions are available: