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

Kai Jin (), Taikun Zhu, Zhaoquan Gu and Xiaoming Sun
Additional contact information
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

Mathematics, 2022, vol. 10, issue 24, 1-18

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.

Keywords: combinatorial design; ordered design; Hamming code; error-correcting code; hat guessing game; Latin matching; antipodal matching; Latin square and hypercube; multiagent system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/24/4703/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/24/4703/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:24:p:4703-:d:1000287

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().