Left to right maxima in Dyck prefixes

Source abstract

In a Dyck path, a peak which is strictly (weakly) higher than all the preceding peaks is called a strict (weak) left-to-right maximum. By dropping the restrictions for the path to end on the $x$-axis, one obtains Dyck prefixes. We obtain explicit generating functions for both weak and strict left-to-right maxima in Dyck prefixes. The proofs of the associated asymptotics make use of analytic techniques such as Mellin transforms, singularity analysis and formal residue calculus. Received: 26 April 2022 | Accepted: 28 June 2023