Stasinski, Alexander and Voll, Christopher (2013) 'A new statistic on the hyperoctahedral groups.', The electronic journal of combinatorics., 20 (3). P50.
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 reversing involutions.
|Keywords:||Hyperoctahedral groups, Signed permutation statistics, Sign reversing involutions, Descent sets, Generating functions.|
|Full text:||(VoR) Version of Record|
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|Publisher Web site:||http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p50|
|Date accepted:||No date available|
|Date deposited:||06 May 2014|
|Date of first online publication:||September 2013|
|Date first made open access:||No date available|
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