A New Statistic on the Hyperoctahedral Groups

作者：Stasinski Alexander^*; Voll Christopher

来源：ELECTRONIC JOURNAL OF COMBINATORICS, 2013, 20(3).

DOI：10.37236/3242

• Hyperoctahedral groups
• signed permutation statistics
• sign reversing involutions
• descent sets
• generating functions

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 Poincare polynomials of the varieties of symmetric matrices of fixed rank. %26lt;br%26gt;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.

• 出版日期2013-9-26