# Proof of a conjecture of Klopsch-Voll on Weyl groups of type $A$

@article{Brenti2017ProofOA, title={Proof of a conjecture of Klopsch-Voll on Weyl groups of type \$A\$}, author={Francesco Brenti and Angela Carnevale}, journal={arXiv: Combinatorics}, year={2017} }

We prove a conjecture of Klopsch-Voll on the signed generating function of a new statistic on the quotients of the symmetric groups. As a consequence of our results we also prove a conjecture of Stasinski-Voll in type $B$.

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## References

SHOWING 1-7 OF 7 REFERENCES

### A New Statistic on the Hyperoctahedral Groups

- MathematicsElectron. J. Comb.
- 2013

A new statistic on the hyperoctahedral groups, and a conjectural formula for its signed distributions over arbitrary descent classes are introduced, which gives the Poincare polynomials of the varieties of symmetric matrices of fixed rank.

### Reflection groups and coxeter groups

- Mathematics
- 1990

Part I. Finite and Affine Reflection Groups: 1. Finite reflection groups 2. Classification of finite reflection groups 3. Polynomial invariants of finite reflection groups 4. Affine reflection groups…

### Enumerative combinatorics

- MathematicsSIGA
- 2008

This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.

### Igusa-type functions associated to finite formed spaces and their functional equations

- Mathematics
- 2006

We study symmetries enjoyed by the polynomials enumerating non-degenerate flags in finite vector spaces, equipped with a non-degenerate alternating bilinear, hermitian or quadratic form. To this end…

### Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B

- Mathematics
- 2011

We study representation zeta functions of finitely generated, torsion-free nilpotent groups which are groups of rational points of unipotent group schemes over rings of integers of number fields.…

### Combinatorics of Coxeter Groups

- Mathematics
- 2005

I.- The basics.- Bruhat order.- Weak order and reduced words.- Roots, games, and automata.- II.- Kazhdan-Lusztig and R-polynomials.- Kazhdan-Lusztig representations.- Enumeration.- Combinatorial…