Europ. J. Combinatorics, 18, 1995, p. 329-355.
Robert J. Clarke and Dominique Foata
Eulerian Calculus, III : The Ubiquitous Cauchy Formula
The purpose of this paper is to calculate
the distributions of several joint statistics on the symmetric
group and related structures that have been studied in the
previous two Eulerian Calculus papers. It is shown how the
Cauchy formula on symmetric functions, an old MacMahon
bijection and a combinatorial lemma on skew-tableaux
provide the necessary ingredients for
calculating those distributions.
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