Cyclic Whist tournaments
A Whist tournament Wh\((4n)\) for \(4n\) players is a schedule of games, each involving two players against two others, so that (i) there are \(4n-1\) rounds, \(n\) games per round, (ii) each player plays in exactly one game per round, (iii) each pair of players partners each other exactly once, (iv) each player opposes every other player exactly twice. A Wh\((4n)\) on \(G\cup\{\infty\}\), where \(G\) is an additive group of order \(4n-1\), is cyclic if round \(g\) is obtained from the first round by adding \(g\) to each entry except \(\infty\). Until 1990 the only cyclic Whist tournaments known were some due to Moore in 1896. In this paper, several infinite families of cyclic Whist tournaments are given, including ones on \(3p^ n+1\) players (where \(p\equiv 1\pmod 4\) is a prime) and on \(7\cdot 5^ n+1\) players.
scientific article; zbMATH DE number 562641