Abstract
In this paper, we construct Room frames with partitionable transversals. Direct and recursive constructions are used to find sets of disjoint complete ordered partitionable (COP) transversals and sets of disjoint holey ordered partitionable (HOP) transversals for Room frames. Our main results include upper and lower bounds on the number of disjoint COP transversals and the number of disjoint HOP transversals for Room frames of type 2n. This work is motivated by the large number of applications of these designs.
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Dinitz, J.H., Lamken, E.R. HOPs and COPs: Room frames with partitionable transversals. Designs, Codes and Cryptography 19, 5–26 (2000). https://doi.org/10.1023/A:1008334412968
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DOI: https://doi.org/10.1023/A:1008334412968