A generalization of rotational tournaments (Q1119595)

An (n,r)-tournament is a set of n vertices such that the vertices in each of the \(\left( \begin{matrix} n\\ r\end{matrix} \right)\) subsets of size r have been assigned one of the r! possible orderings. Such a tournament is rotational if it has an automorphism which permutes the vertices in a cycle of length n. The authors show that if \(n\geq r\geq 2\) then there exists a rotational (n,r)-tournament if and only if \(g.c.d.(n,r)=1\).