The Descent Set and Connectivity Set of a Permutation
Combinatorics
2007-05-23 v1
Abstract
The descent set D(w) of a permutation w of 1,2,...,n is a standard and well-studied statistic. We introduce a new statistic, the connectivity set C(w), and show that it is a kind of dual object to D(w). The duality is stated in terms of the inverse of a matrix that records the joint distribution of D(w) and C(w). We also give a variation involving permutations of a multiset and a q-analogue that keeps track of the number of inversions of w.
Cite
@article{arxiv.math/0507224,
title = {The Descent Set and Connectivity Set of a Permutation},
author = {Richard P. Stanley},
journal= {arXiv preprint arXiv:math/0507224},
year = {2007}
}
Comments
12 pages