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Equi-distribution over descent classes of the hyperoctahedral group. (English) Zbl 1095.05001

Summary: A classical result of MacMahon shows that the length function and the major index are equi-distributed over the symmetric group. D. Foata and M.-P. Schützenberger [Math. Nachr. 83, 143–159 (1978; Zbl 0319.05002)] gave a remarkable refinement and proved that these parameters are equi-distributed over inverse descent classes, implying bivariate equi-distribution identities. Type B analogues of these results, refinements and consequences are given in this paper.

MSC:

05A05 Permutations, words, matrices
05A15 Exact enumeration problems, generating functions

Citations:

Zbl 0319.05002
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References:

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