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The paper presents a description of the results of computational experiments aimed at constructing heuristic approximations of the spectra of the number of intercalates in the Latin squares and diagonal Latin squares of orders 10–28. Starting from orders 18–20, the calculations become computationally complex and require the using of distributed computing systems. The heuristic approximations of the spectra obtained as a result of the computational experiments made it possible to impose the strongest upper and lower bounds known to date on the corresponding terms of the numerical series A307163, A307164, and A345760 (for diagonal Latin squares) and A092237 and A368182 (for Latin squares) in the OEIS.

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Construction of Intercalate Number Spectra in Latin Squares of Orders 18–28 Using Distributed Parallel Software Implementations of Heuristic Methods

  • 会议论文

  • 发表日期：

    2026年

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  • Eduard Vatutin,
  • Jia Wei-Ting,
  • Jun Chi Ma,
  • Qiang Miao,
  • Maxim Manzyuk,
  • Natalia Kukushkina,
  • Ilya Kurochkin,
  • Alexander Albertian

摘要

The paper presents a description of the results of computational experiments aimed at constructing heuristic approximations of the spectra of the number of intercalates in the Latin squares and diagonal Latin squares of orders 10–28. Starting from orders 18–20, the calculations become computationally complex and require the using of distributed computing systems. The heuristic approximations of the spectra obtained as a result of the computational experiments made it possible to impose the strongest upper and lower bounds known to date on the corresponding terms of the numerical series A307163, A307164, and A345760 (for diagonal Latin squares) and A092237 and A368182 (for Latin squares) in the OEIS.