New infinite classes of Z-cyclic whist tournaments - Finizio, Norman J. (Utilitas Mathematica, 1998)
Let q1, q2, p1, . . . pn denote primes, qi ≡ 3 (mod 4), pi ≡ 1 (mod 4). In this study we establish the following: (1) if there exists a Z-cyclic whist tournament on q21 players and if there exists a Z-cyclic whist tournament on q22 players then there exists a Z-cyclic whist tournament on q21q22 players and (2) if there exists a Z-cyclic whist tournament on q21q22 players then there exists a Z-cyclic whist tournament on q21q22∏ni = 1pαii for all n ≥ 1, αi ≥ 0, i = 2, . . . , n. These results extend the knowledge of the existence of Z-cyclic whist tournaments and also that of several other related designs, in particular Z-cyclic (v, 4, 1)-resolvable perfect Mendelsohn designs.