Let Sn be the symmetric group of permutations π = π1π2 · · ·πn of {1, 2, . . . , n}. An index i of π is a peak if πi−1 < πi > πi+1, and we let P (π) denote the set of peaks of π. Given any set S of positive integers, we define PS(n) = {π ∈ Sn : P (π) = S}. Burdzy, Sagan, and the first author showed that for all fixed subsets of positive integers S and sufficiently large n we have |PS(n)| = pS(n...
