Europ. J. Combinatorics, 18, 1995, p. 329-355.

Robert J. Clarke and Dominique Foata

Eulerian Calculus, III : The Ubiquitous Cauchy Formula

Abstract. 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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