Directedordered whist tournaments and (v,5,1) difference families: existence results and some new classes of Z-cyclic solutions
In this paper a new specialization of whist tournament is introduced, namely a directedordered whist tournament. It is established that directedordered whist tournaments do not exist when the number of players,v, equals 4n and that directedordered whist tournaments exist for all v=4n+1. Several new (v,5,1) difference families are given and are combined with a construction of Buratti and Zuanni to produce Z-cyclic directedordered whist tournaments. Infinite families of Z-cyclic directedordered whist tournaments are obtained by applying the product theorems of Anderson et al. to these latter designs together with the classic whist construction of Baker which is shown to produce directedordered whist designs. In addition many new examples of Z-cyclic directed whist tournaments and ordered whist tournaments are given.
directedordered whist tournaments whist tournaments difference families directed whist tournaments ordered whist tournaments almost difference families z-cyclic designs resolvable bibds near resolvable bibds