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Latin Matchings and Ordered Designs OD(n−1, n, 2n−1)
- Source :
- Mathematics, Vol 10, Iss 24, p 4703 (2022)
- Publication Year :
- 2022
- Publisher :
- MDPI AG, 2022.
-
Abstract
- This paper revisits a combinatorial structure called the large set of ordered design (LOD). Among others, we introduce a novel structure called Latin matching and prove that a Latin matching of order n leads to an LOD(n−1, n, 2n−1); thus, we obtain constructions for LOD(1, 2, 3), LOD(2, 3, 5), and LOD(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, 2n−2); therefore, the order of a Latin matching must be prime. We also show some applications in multiagent systems.
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 24
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.fc3929db0e41979fa81d7dbbcdd5ad
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/math10244703