A New Statistic on the Hyperoctahedral Groups

Stasinski A, Voll C (2013)
The Electronic Journal of Combinatorics 20(3): P50 .

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Stasinski, Alexander; Voll, ChristopherUniBi
Abstract / Bemerkung
We introduce a new statistic on the hyperoctahedral groups (Coxeter groups of type B), and give a conjectural formula for its signed distributions over arbitrary descent classes.  The statistic is analogous to the classical Coxeter length function, and features a parity condition. For descent classes which are singletons the conjectured formula gives the Poincaré polynomials of the varieties of symmetric matrices of fixed rank.For several descent classes we prove the conjectural formula. For this we construct suitable supporting sets for the relevant generating functions. We prove cancellations on the complements of these supporting sets using suitably defined sign reversinginvolutions.
Erscheinungsjahr
2013
Zeitschriftentitel
The Electronic Journal of Combinatorics
Band
20
Ausgabe
3
Art.-Nr.
P50
eISSN
1077-8926
Page URI
https://pub.uni-bielefeld.de/record/2963574

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Stasinski A, Voll C. A New Statistic on the Hyperoctahedral Groups. The Electronic Journal of Combinatorics. 2013;20(3): P50 .
Stasinski, A., & Voll, C. (2013). A New Statistic on the Hyperoctahedral Groups. The Electronic Journal of Combinatorics, 20(3), P50 . https://doi.org/10.37236/3242
Stasinski, A., and Voll, C. (2013). A New Statistic on the Hyperoctahedral Groups. The Electronic Journal of Combinatorics 20:P50 .
Stasinski, A., & Voll, C., 2013. A New Statistic on the Hyperoctahedral Groups. The Electronic Journal of Combinatorics, 20(3): P50 .
A. Stasinski and C. Voll, “A New Statistic on the Hyperoctahedral Groups”, The Electronic Journal of Combinatorics, vol. 20, 2013, : P50 .
Stasinski, A., Voll, C.: A New Statistic on the Hyperoctahedral Groups. The Electronic Journal of Combinatorics. 20, : P50 (2013).
Stasinski, Alexander, and Voll, Christopher. “A New Statistic on the Hyperoctahedral Groups”. The Electronic Journal of Combinatorics 20.3 (2013): P50 .

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