The sorting index
Combinatorics
2010-10-25 v2
Abstract
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.
Cite
@article{arxiv.1007.1207,
title = {The sorting index},
author = {T. Kyle Petersen},
journal= {arXiv preprint arXiv:1007.1207},
year = {2010}
}
Comments
14 pages, minor changes, new references added