Directed–ordered whist tournaments and (v,5,1) difference families: existence results and some new classes of Z-cyclic solutions Original Research Article

In this paper a new specialization of whist tournament is introduced, namely a directed–ordered whist tournament. It is established that directed–ordered whist tournaments do not exist when the number of players,v, equals 4n and that directed–ordered 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 directed–ordered whist tournaments. Infinite families of Z-cyclic directed–ordered 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 directed–ordered whist designs. In addition many new examples of Z-cyclic directed whist tournaments and ordered whist tournaments are given.