IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i8p1207-d1377469.html
   My bibliography  Save this article

Combinatorial Generation Algorithms for Directed Lattice Paths

Author

Listed:
  • Yuriy Shablya

    (Laboratory of Algorithms and Technologies for Discrete Structures Research, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia)

  • Arsen Merinov

    (Laboratory of Algorithms and Technologies for Discrete Structures Research, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia)

  • Dmitry Kruchinin

    (Laboratory of Algorithms and Technologies for Discrete Structures Research, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia)

Abstract

Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified properties. This article is devoted to issues related to the construction of such combinatorial generation algorithms for a wide class of directed lattice paths. The main method used is based on the representation of a given combinatorial set in the form of an AND/OR tree structure. To apply this method, it is necessary to have an expression for the cardinality function of a combinatorial set that satisfies certain requirements. As the main result, we have found recurrence relations for enumerating simple directed lattice paths that satisfy the requirements of the applied method and have constructed the corresponding AND/OR tree structure. Applying the constructed AND/OR tree structure, we have developed new algorithms for ranking and unranking simple directed lattice paths. Additionally, the obtained results were generalized to the case of directed lattice paths.

Suggested Citation

  • Yuriy Shablya & Arsen Merinov & Dmitry Kruchinin, 2024. "Combinatorial Generation Algorithms for Directed Lattice Paths," Mathematics, MDPI, vol. 12(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1207-:d:1377469
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/8/1207/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/8/1207/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1207-:d:1377469. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.