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

Reiner, Victor

Eur. J. Comb. 14, No. 6, 569-579 (1993).

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

Keywords:

multivariate generating function; signed permutations; descent statistics; Gessel’s necklace bijection

Citations:

Zbl 0793.05004