Left to right maxima in Dyck prefixes

Authors

  • Arnold Knopfmacher The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa https://orcid.org/0000-0003-1962-043X
  • Aubrey Blecher The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa https://orcid.org/0000-0003-2487-3220

DOI:

https://doi.org/10.13069/jacodesmath.v11i1.248

Keywords:

Dyck prefixes, Generating functions, Asymptotic

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

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Published

2023-10-06

How to Cite

Knopfmacher, A. ., & Blecher, A. (2023). Left to right maxima in Dyck prefixes. Journal of Algebra Combinatorics Discrete Structures and Applications, 11(1), 1–13. https://doi.org/10.13069/jacodesmath.v11i1.248

Issue

Vol. 11 Issue 1: January 2024

Section

Articles