Problem of the Week
Hilton Memorial Lecture
A Dyck word is a string in the letters X and Y with n X's, n Y's, such that no initial sub-word has more Y's than X's. Each Dyck word gives rise to a path (a Dyck path) in the xy-plane having only North-East steps and South-East steps. We construct a formal power series on several variables that encodes many statistics on non-decreasing Dyck paths. In particular, we use this formal power series to count peaks, and indexed sums of pyramid weights, for all non-decreasing Dyck paths of length 2n.