Séminaire Lotharingien de Combinatoire, 87B.5 (2023), 12 pp.

Aubrey Blecher and Arnold Knopfmacher

Left-to-right maxima in Dyck paths

Abstract. In a Dyck path a peak which is (weakly) higher than all the preceding peaks is called a strict (weak) left-to-right maximum. We obtain explicit generating functions for both weak and strict left-to-right maxima in Dyck paths. The proofs of the associated asymptotics make use of analytic techniques such as Mellin transforms, singularity analysis and formal residue calculus.

Received: July 21, 2021. Revised: August 9, 2023. Published: August 31, 2023.

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If you need to cite this article, here is a bibtex:

@article{BlecherKnopfmacher23,
author = {Blecher, Aubrey and Arnold Knopfmacher, Arnold},
title = {{Left-to-right maxima in Dyck paths}},
fjournal = {S{\'e}minaire Lotharingien de Combinatoire},
journal = {S{\'e}min. Lothar. Combin.},
issn={1286-4889},
volume = {87B},
number= {5},
pages = {1--12},
year = {2023},
language = {English},
doi={10.48550/arXiv.2107.03102},
}