A Few More $Z$-Cyclic Whist Tournaments

Abstract

$Z$-cyclic whist tournaments for $q+1$ players, $Wh(q+1)$, where $q$ is a prime, $q\equiv 3(\mathrm{mod}4)$, are quite rare. Solutions for $q=3,7,11,19,23,$ and $31$ were known in the early to mid 1890’s. Since that time no new such $Wh(q+1)$ have appeared.
Here we present $Z$-cyclic $Wh(q+1)$ for $q=43,47,59$. Also presented for the first time is a $Z$-cyclic $Wh(45)$ and a $Z$-cyclic $Wh(40)$ that has the three person property. All of these results were obtained via the computer.