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In a Dyck path a peak which is (weakly) higher than all the preceding peaksis called a strict (weak) left to right maximum. We obtain explicit generatingfunctions for both weak and strict left to right maxima in Dyck paths. Theproofs of the associated asymptotics make use of analytic techniques such asMellin transforms, singularity analysis and formal residue calculus.

Left to right maxima in Dyck Paths