The location of the first maximum in the first sojourn of a Dyck path

Helmut Prodinger

doi:10.46298/dmtcs.426

Article

The location of the first maximum in the first sojourn of a Dyck path

Helmut Prodinger⁽¹⁾⁽²⁾

(1) Department of Mathematical Sciences [Matieland, Stellenbosch Uni.]

(2) Department of Mathematical Sciences [Stellenbosch University]

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March 26, 2015

Published on

January 1, 2008

Last modified on

March 31, 2025

Volume 10

vol. 10:3

Analysis of Algorithms

DOI

10.46298/dmtcs.426

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The location of the first maximum in the first sojourn of a Dyck path

Helmut Prodinger⁽¹⁾⁽²⁾

(1) Department of Mathematical Sciences [Matieland, Stellenbosch Uni.]

(2) Department of Mathematical Sciences [Stellenbosch University]

Abstract

For Dyck paths (nonnegative symmetric) random walks, the location of the first maximum within the first sojourn is studied. Generating functions and explicit resp. asymptotic expressions for the average are derived. Related parameters are also discussed.

Keywords