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Signed permutation statistics. (English) Zbl 0793.05005
Summary: We derive multivariate generating functions that count signed permutations by various statistics, using the hyperoctahedral generalization of methods of Garsia and Gessel. We also derive the distributions over inverse descent classes of signed permutations for two of these statistics individually (the major index and inversion number). These results show that, in contrast to the case for (unsigned) permutations, these two statistics are not generally equidistributed. We also discuss applications to statistics on the wreath product \(C_ k\wr S_ n\) of a cyclic group with the symmetric group.

05A15 Exact enumeration problems, generating functions
05A05 Permutations, words, matrices
06A07 Combinatorics of partially ordered sets
05E15 Combinatorial aspects of groups and algebras (MSC2010)
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