# Upper Binomial Posets and Signed Permutation Statistics

@article{Reiner1993UpperBP, title={Upper Binomial Posets and Signed Permutation Statistics}, author={Victor Reiner}, journal={Eur. J. Comb.}, year={1993}, volume={14}, pages={581-588} }

Abstract We derive generating functions counting signed permutations by two statistics, using a hyperoctahedral analogue of the binomial poset technique of Stanley [7].

## 40 Citations

### Binomial posets with non-isomorphic intervals

- Mathematics
- 2005

The confluent binomial posets with the atomic function A(n) = max (1,2^(n-2)) are classified. In particular, it is shown that in general there are non-isomorphic intervals of the same length.

### EULER-MAHONIAN PARAMETERS ON COLORED

- Mathematics
- 2004

New combinatorial statistics on colored permutation groups are introduced here. We present two dierent generaliza- tions of major index and descent number, one of them is com- binatorial in nature…

### EULER-MAHONIAN PARAMETERS ON COLORED PERMUTATION GROUPS

- Mathematics
- 2004

New combinatorial statistics on colored permutation groups are introduced here. We present two different generalizations of major index and descent number, one of them is combinatorial in nature and…

### Euler-Mahonian parameters on colored permutation groups.

- Mathematics
- 2004

New combinatorial statistics on colored permutation groups are introduced here. We present two different generalizations of major index and descent number, one of them is combinatorial in nature and…

### Signed Words and Permutations II; The Euler-Mahonian Polynomials

- MathematicsElectron. J. Comb.
- 2005

Two approaches are here systematically explored, using the flag-major index on the one hand, and theFlag-inversion number on the other hand, of calculating multivariable generating functions for this group by statistics involving record values and the length function.

### Calcul Basique des Permutations Signées

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- 1997

The traditional basic calculus on permutation statistic distributions is extended to the case of signed permutations.Le calcul basique classique sur les distributions des statistiques de permutations…

### Signed words and permutations, IV: Fixed and pixed points

- Mathematics
- 2006

The flag-major index “fmaj” and the classical length function “ℓ” are used to construct two q-analogs of the generating polynomial for the hyperoctahedral group Bn by number of positive and negative…

### SIGNED WORDS AND PERMUTATIONS, II;

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As for the symmetric group of ordinary permutations there is also a statistical study of the group of signed permutations, that consists of calculating multivariable generating functions for this…

### Weyl-Mahonian Statistics for Weighted Flags of Type A-D.

- Mathematics
- 2018

We relate properties of weighted flags (or multiflags) of type AD to statistics of the corresponding Weyl groups. For type A, we recover the Mahonian statistics on symmetric groups. Finally, we…