Enumeration of Isotopy Classes of Diagonal Latin Squares of Small Order Using Volunteer Computing

  • Eduard VatutinEmail author
  • Alexey Belyshev
  • Stepan Kochemazov
  • Oleg Zaikin
  • Natalia Nikitina
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 965)


The paper is devoted to discovering new features of diagonal Latin squares of small order. We present an algorithm, based on a special kind of transformations, that constructs a canonical form of a given diagonal Latin square. Each canonical form corresponds to one isotopy class of diagonal Latin squares. The algorithm was implemented and used to enumerate the isotopy classes of diagonal Latin squares of order at most 8. For order 8 the computational experiment was conducted in a volunteer computing project. The algorithm was also used to estimate how long it would take to enumerate the isotopy classes of diagonal Latin squares of order 9 in the same volunteer computing project.


Volunteer computing Combinatorics Latin square Diagonal Latin square Enumeration 



The research was partially supported by Russian Foundation for Basic Research (grants 16-07-00155-a, 17-07-00317-a, 18-07-00628-a, 18-37-00094-mol-a) and by Council for Grants of the President of the Russian Federation (stipend SP-1829.2016.5).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Eduard Vatutin
    • 1
    Email author
  • Alexey Belyshev
    • 2
  • Stepan Kochemazov
    • 3
  • Oleg Zaikin
    • 3
  • Natalia Nikitina
    • 4
  1. 1.Southwest State UniversityKurskRussia
  2. 2.BOINC.ruMoscowRussia
  3. 3.Matrosov Institute for System Dynamics and Control Theory SB RASIrkutskRussia
  4. 4.Institute of Applied Mathematical Research KRC RASPetrozavodskRussia

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