Necessary conditions and frame constructions for ZZ-cyclic patterned starter whist tournaments

The whist tournament problem has attracted the interests of many design theorists for over a century. To construct ZZ-cyclic whist tournaments, the concept of ZZ-cyclic patterned starter whist tournaments was introduced. The research on ZZ-cyclic patterned starter whist tournaments dates back to 1954. Although considerable progress has been made in the last decade or so, less has been made about the existence of ZZ-cyclic patterned starter whist tournaments, despite the efforts of many authors.In this paper, we will first provide two new nonexistence results for ZZ-cyclic patterned starter whist tournaments. Then, we will propose a general recursive construction, i.e., a frame construction, for ZZ-cyclic patterned starter whist tournaments. As a consequence, we are able to unify many known constructions for ZZ-cyclic patterned starter whist tournaments. The known existence results of such designs are then extended.