|Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.8|
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.
(Concerned with sequence A003319 .)
Received July 18 2005; revised version received August 16 2005. Published in Journal of Integer Sequences, August 24 2005.