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Latin Matchings and Ordered Designs OD ( n −1, n , 2 n −1)

Author

Listed:
  • Kai Jin

    (School of Intelligent Systems Engineering, Shenzhen Campus of Sun Yat-sen University, Shenzhen 518107, China)

  • Taikun Zhu

    (School of Intelligent Systems Engineering, Shenzhen Campus of Sun Yat-sen University, Shenzhen 518107, China)

  • Zhaoquan Gu

    (School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China)

  • Xiaoming Sun

    (Institute of computing technology, Chinese Academy of Sciences, Beijing 100864, China)

Abstract

This paper revisits a combinatorial structure called the large set of ordered design ( L O D ). Among others, we introduce a novel structure called Latin matching and prove that a Latin matching of order n leads to an L O D ( n − 1 , n , 2 n − 1 ) ; thus, we obtain constructions for L O D ( 1 , 2 , 3 ) , L O D ( 2 , 3 , 5 ) , and L O D ( 4 , 5 , 9 ) . Moreover, we show that constructing a Latin matching of order n is at least as hard as constructing a Steiner system S ( n − 2 , n − 1 , 2 n − 2 ) ; therefore, the order of a Latin matching must be prime. We also show some applications in multiagent systems.

Suggested Citation

  • Kai Jin & Taikun Zhu & Zhaoquan Gu & Xiaoming Sun, 2022. "Latin Matchings and Ordered Designs OD ( n −1, n , 2 n −1)," Mathematics, MDPI, vol. 10(24), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4703-:d:1000287
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