Z-cyclic whist tournaments with a patterned starter initial round
Discrete Applied Mathematics
Finite fields
More ZCPS-Wh(v) and several new infinite classes of Z-cyclic whist tournaments
Discrete Applied Mathematics
New product theorems for Z-cyclic whist tournaments
Journal of Combinatorial Theory Series A
General frame constructions for Z-cyclic triplewhist tournaments
Journal of Combinatorial Theory Series A
Note: Necessary conditions for the existence of two classes of ZCPS-Wh(v)
Discrete Applied Mathematics
Combinatorial designs and the theorem of Weil on multiplicative character sums
Finite Fields and Their Applications
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The whist tournament problem has attracted the interests of many design theorists for over a century. To construct Z-cyclic whist tournaments, the concept of Z-cyclic patterned starter whist tournaments was introduced. The research on Z-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 Z-cyclic patterned starter whist tournaments, despite the efforts of many authors. In this paper, we will first provide two new nonexistence results for Z-cyclic patterned starter whist tournaments. Then, we will propose a general recursive construction, i.e., a frame construction, for Z-cyclic patterned starter whist tournaments. As a consequence, we are able to unify many known constructions for Z-cyclic patterned starter whist tournaments. The known existence results of such designs are then extended.