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.
Funder
National Natural Science Foundation of China
Shenzhen Science and Technology Program
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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