\(\mathbb Z\)-cyclic \(\mathrm{wh}(28)\) (Q2839742)

A \(v\)-player Whist tournament Wh\((v)\) is a schedule of games, each involving two players opposing two others. Every round, the players are partitioned into games, with at most one player left over. Each player partners every other player exactly once and opposes every other player exactly twice during the tournament. Whist tournaments are known to exist for all \(v\equiv0,1\pmod4\). A whist tournament is said to be \(\mathbb{Z}\)-cyclic if the players are elements in \(\mathbb{Z}_N\cup A\), where \(N = v\), \(A =\emptyset\) if \(v\equiv1\pmod4\) and \(N = v-1\), \(A = \{\infty\}\) if \(v\equiv0\pmod4\). While all \(\mathbb{Z}\)-cyclic Wh\((v)\) design are classified for all \(v\equiv0,1\pmod4\) with \(v\leq25\), the paper reports on all \(\mathbb{Z}\)-cyclic Wh\((28)\). It is shown that there are 7,910,127 \(\mathbb{Z}\)-cyclic Wh\((28)\). Specializations related to a 28-player \(\mathbb{Z}\)-cyclic whist designs are also enumerated.