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.
@article{10_37236_3242,
author = {Alexander Stasinski and Christopher Voll},
title = {A new statistic on the hyperoctahedral groups},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {3},
doi = {10.37236/3242},
zbl = {1295.05038},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3242/}
}
TY - JOUR
AU - Alexander Stasinski
AU - Christopher Voll
TI - A new statistic on the hyperoctahedral groups
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/3242/
DO - 10.37236/3242
ID - 10_37236_3242
ER -
%0 Journal Article
%A Alexander Stasinski
%A Christopher Voll
%T A new statistic on the hyperoctahedral groups
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/3242/
%R 10.37236/3242
%F 10_37236_3242
Alexander Stasinski; Christopher Voll. A new statistic on the hyperoctahedral groups. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/3242
