论文标题
在有限根系中的广义下降和广义反演的中心限制定理
Central limit theorems for generalized descents and generalized inversions in finite root systems
论文作者
论文摘要
我们考虑有限的Weyl组中的广义倒置和下降。我们建立了正根的指标随机变量的Coxeter理论特性，例如两个此类指标随机变量的协方差。然后，我们计算经典类型中广义反转和下降的方差。最终，我们使用依赖关系图来证明根本poset中的一般抗小节的中心限制定理，尤其是广义下降，然后是广义反演。
We consider generalized inversions and descents in finite Weyl groups. We establish Coxeter-theoretic properties of indicator random variables of positive roots such as the covariance of two such indicator random variables. We then compute the variances of generalized inversions and descents in classical types. We finally use the dependency graph method to prove central limit theorems for general antichains in root posets and in particular for generalized descents, and then for generalized inversions.
