Fix-Mahonian Calculus III; a Quadruple Distribution

Details Fix-Mahonian Calculus III; a Quadruple Distribution Fix-Mahonian Calculus III; a Quadruple Distribution

2007-03-15

arxiv.org/abs/math/0703454v1

Mathematics

Combinatorics

26 pages

Scientific paper

A four-variable distribution 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.

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