Enumerative combinatorics
European Journal of Combinatorics
Signed permutation statistics and cycle type
European Journal of Combinatorics
Upper binomial posets and signed permutation statistics
European Journal of Combinatorics
Permutation statistics of indexed permutations
European Journal of Combinatorics
Eulerian calculus, I: univariable statistics
European Journal of Combinatorics
Eulerian calculus, II: an extension of Han's fundamental transformation
European Journal of Combinatorics
Eulerian calculus, III: the ubiquitous Cauchy formula
European Journal of Combinatorics
Journal of Computational and Applied Mathematics
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The flag major index and group actions on polynomial rings
European Journal of Combinatorics
Descent Numbers and Major Indices for the Hyperoctahedral Group
Advances in Applied Mathematics
Rook Theory for Perfect Matchings
Advances in Applied Mathematics
Equi-distribution over descent classes of the hyperoctahedral group
Journal of Combinatorial Theory Series A
Kernel method and system of functional equations
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
We introduce a natural extension of Adin, Brenti, and Roichman's major-index statistic nmaj on signed permutations (Adv. Appl. Math. 27 (2001) 210-224) to wreath products of a cyclic group with the symmetric group. We derive "insertion lemmas" which allow us to give simple bijective proofs that our extension has the same distribution as another statistic on wreath products introduced by Adin and Roichman (European J. Combin. 22 (2001) 431-446) called the flag major index. We also use our insertion lemmas to show that nmaj, the flag major index, and an inversion statistic have the same distribution on a subset of signed permutations in bijection with perfect matchings. We show that this inversion statistic has an interpretation in terms of q-counting rook placements on a shifted Ferrers board.Many results on permutation statistics extend to results on multiset permutations (words). We derive a number of analogous results for signed words, and also words with higher-order roots of unity attached to them.