Abstract

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.

Author Keywords: Whist tournaments; Directed whist tournaments; Ordered whist tournaments; Directed–ordered whist tournaments; Difference families; Almost difference families; Z-cyclic designs; Resolvable BIBDs; Near resolvable BIBDs

Article Outline

1. Introduction

2. Existence results

3. (v,5,1) Difference families

3.1. Type 1: DFs with no multipliers for v221

3.2. Type 2: DFs for v=q², q prime

3.3. Type 3: DFs with other multipliers

4. Infinite classes of Z-cyclic solutions

5. Some new Z-cyclic solutions

References