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Signed permutation statistics and cycle type. (English) Zbl 0793.05006

Summary: We derive a multivariate generating function which counts signed permutations by their cycle type and two other descent statistics, analogous to a result of I. Gessel and C. Reutenauer [J. Comb. Theory, Ser. A 64, No. 2, 189-215 (1993; Zbl 0793.05004)] for (unsigned) permutations. The derivation uses a bijection which is the hyperoctahedral analogue of Gessel’s necklace bijection.

MSC:

05A15 Exact enumeration problems, generating functions
05A05 Permutations, words, matrices
11A25 Arithmetic functions; related numbers; inversion formulas

Citations:

Zbl 0793.05004
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