Volume 28 • Number 2 • 2006   • Compatible Factorizations and Three-fold Triple Systems Haslinda Ibrahim Abstract. A three-fold triple system is a design wherein each pair of treatments occurs exactly once. One way to construct this design is by using an idempotent commutative quasigroup. This paper attempts to provide another method of constructing a 3-fold triple system. Firstly, we would like to discuss compatible factorization without multiple edges using a patterned starter construction. Then, we will use this construction to enumerate a distinct 3-fold triple system for every odd order v>3. 2000 Mathematics Subject Classification: 05B05, 68R05, 68R10. Full text: PDF