Eulerian calculus. III: The ubiquitous Cauchy formula. (English) Zbl 0826.05058

Summary: 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 [ibid. 15, No. 4, 345-362 (1994; Zbl 0811.05069) and ibid. 16, No. 3, 221-252 (1995; Zbl 0822.05066)]. 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.


05E15 Combinatorial aspects of groups and algebras (MSC2010)
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
05A05 Permutations, words, matrices
Full Text: DOI


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