The Descent Set and Connectivity Set of a Permutation

Details The Descent Set and Connectivity Set of a Permutation The Descent Set and Connectivity Set of a Permutation

2005-07-11

arxiv.org/abs/math/0507224v1

Mathematics

Combinatorics

12 pages

Scientific paper

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.

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