%0 Journal Article
%T The sorting index
%A T. Kyle Petersen
%J Mathematics
%D 2010
%I arXiv
%X We consider a bivariate polynomial that generalizes both the length and reflection length generating functions in a finite Coxeter group. In seeking a combinatorial description of the coefficients, we are led to the study of a new Mahonian statistic, which we call the sorting index. The sorting index of a permutation and its type B and type D analogues have natural combinatorial descriptions which we describe in detail.
%U http://arxiv.org/abs/1007.1207v2