Directed–ordered whist tournaments and (v,5,1) difference families: existence results and some new classes of Z-cyclic solutions
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- 作者：Julian ; R. ; Abel ; R. ; Costa ; Stephanie ; Finizio ; Norman J.
- 关键词：Whist tournaments ; Directed whist tournaments ; Ordered whist tournaments ; Directed&ndash ; ordered whist tournaments ; Difference families ; Almost difference families ; Z-cyclic designs ; Resolvable BIBDs ; Near resolvable BIBDs
- 刊名：Discrete Applied Mathematics
- 出版年：2004
- 出版时间：September 30, 2004
- 年：2004
- 卷：143
- 期：1-3
- 页码：43-53
- 全文大小：232 K
文摘
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.