General results on the enumeration of strings in Dyck paths
type: Item
instance of: scholarly article
title: General results on the enumeration of strings in Dyck paths
zbMATH Open document ID: 1217.05028
published in: The Electronic Journal of Combinatorics
publication date: 2011-06-01T00:00:00Z
full work available at URL: https://eudml.org/doc/233021
full work available at URL: v18i1p74.html
review text: Summary: Let \(\tau\) be a fixed lattice path (called in this context string) on the integer plane, consisting of two kinds of steps. The Dyck path statistic ``number of occurrences of \(\tau \)'' has been studied by many authors, for particular strings only. In this paper, arbitrary strings are considered. The associated generating function is evaluated when \(\tau\) is a Dyck prefix (or a Dyck suffix). Furthermore, the case when \(\tau \) is neither a Dyck prefix nor a Dyck suffix is considered, giving some partial results. Finally, the statistic ``number of occurrences of \(\tau\) at height at least \(j\)'' is considered, evaluating the corresponding generating function when \(\tau\) is either a Dyck prefix or a Dyck suffix.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 5903004
author: K. Manes
author: A. Sapounakis
author: I. Tasoulas
author: P. Tsikouras
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5903004