  The peak set of a permutation records the indices of its peaks. These sets
have been studied in a variety of contexts, including recent work by Billey,
Burdzy, and Sagan, which enumerated permutations with prescribed peak sets. In
this article, we look at a natural analogue of the peak set of a permutation,
instead recording the values of the peaks. We define the "pinnacle set" of a
permutation w to be the set {w(i) : i is a peak of w}. Although peak sets and
pinnacle sets mark the same phenomenon for a given permutation, the behaviors
of these sets differ in notable ways as distributions over the symmetric group.
In the work below, we characterize admissible pinnacle sets and study various
enumerative questions related to these objects.
