The sorting index

Details The sorting index The sorting index

2010-07-07

arxiv.org/abs/1007.1207v2

Mathematics

Combinatorics

14 pages, minor changes, new references added

Scientific paper

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.

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