  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.
