New infinite classes of Z-cyclic whist tournaments

Abstract

Let q₁, q₂, p₁, . . . p_n denote primes, q_i ≡ 3 (mod 4), p_i ≡ 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∏ⁿ_{i = 1}p^αi_i for all n ≥ 1, α_i ≥ 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.