Skolem and Rosa rectangles and related designs

We introduce several new constructions for Skolem and Rosa rectangles then we apply them to generate simple cyclic triple systems and disjoint cyclic triple systems. For example, for certain constants C1, C2 we obtain ⌊log3(2n+C1)⌋+C2 disjoint Skolem sequences of order n. Finally, we obtain the analogous results for hooked Skolem and Rosa sequences.