IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1185-d1083052.html
   My bibliography  Save this article

On the Construction of Pandiagonal Magic Cubes

Author

Listed:
  • Fucheng Liao

    (School of Mathematics and Physics, Hechi University, Guangxi 546300, China
    School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China)

  • Hao Xie

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

Abstract

This paper investigates the construction method of pandiagonal magic cube. First, we define a pandiagonal Latin cube. According to this definition, the cube can be constructed by simple methods. After designing a set of orthogonal pandiagonal Latin cubes, the corresponding order pandiagonal magic cube can be constructed. In addition, we give the algebraic conditions of the universal diagonal Latin cube orthogonality and the strict theoretical proof. Based on the proposed method, it can be shown that at least 6 ( n ! ) 3 pandiagonal magic cubes of order n is formed through a pandiagonal Latin cube. Moreover, our method is easy to implement by computer program.

Suggested Citation

  • Fucheng Liao & Hao Xie, 2023. "On the Construction of Pandiagonal Magic Cubes," Mathematics, MDPI, vol. 11(5), pages 1-23, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1185-:d:1083052
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1185/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1185/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Can Hu & Fengchu Pan, 2024. "New Infinite Classes for Normal Trimagic Squares of Even Orders Using Row–Square Magic Rectangles," Mathematics, MDPI, vol. 12(8), pages 1-17, April.

    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:11:y:2023:i:5:p:1185-:d:1083052. 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.