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  1. Home > Articles & Issues >
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  3. Generating functions ...
Conference paper

Generating functions for the area below some lattice paths

Donatella Merlini (1)
(1) Dipartimento di Sistemi e Informatica
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Imported on
May 10, 2017
Published on
December 31, 2002
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Proceedings
DOI
10.46298/dmtcs.3323
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https://about.hal.science/hal-authorisation-v1
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Generating functions for the area below some lattice paths

Donatella Merlini (1)
(1) Dipartimento di Sistemi e Informatica
Abstract
We study some lattice paths related to the concept ofgenerating trees. When the matrix associated to this kind of trees is a Riordan array $D=(d(t),h(t))$, we are able to find the generating function for the total area below these paths expressed in terms of the functions $d(t)$ and $h(t)$.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
  • Generating functions
  • Riordan arrays
  • lattice paths
  • generating trees
  • area
  • internal path length.
Cited by

Source: OpenCitations

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    Journal reference : Volume 309, 2008, pp. 3936-3953

    DOI : 10.1016/j.disc.2008.11.020

  • On Computing the Total Displacement Number via Weighted Motzkin Paths

    arXiv (Cornell University)

    Authors : Andreas Bärtschi, Barbara Geissmann, Daniel Graf, Tomas Hruz, Paolo Penna, Thomas Tschager

    Journal reference : Volume , 2016, pp. 423-434

    DOI : 10.1007/978-3-319-44543-4_33

  • Proper generating trees and their internal path length

    Discrete Applied Mathematics

    Authors : Donatella Merlini ORCID

    Journal reference : Volume 156, 2007, pp. 627-646

    DOI : 10.1016/j.dam.2007.08.051
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