New Z-cyclic triplewhist frames and triplewhist tournament designs

作者：Abel R Julian R; Finizio Norman J; Ge Gennian^*; Greig Malcolm

来源：Discrete Applied Mathematics, 2006, 154(12): 1649-1673.

DOI：10.1016/j.dam.2006.03.001

• whist tournaments
• Z-cyclic designs
• resolvable BIBDs
• near resolvable BIBDs
• triplewhist designs
• Z-cyclic frames
• Z-cyclic triplewhist frames
• cyclic difference matrices

Triplewhist tournaments are a specialization of whist tournament designs. The spectrum for triplewhist tournaments on v players is nearly complete. It is now known that triplewhist designs do not exist for nu = 5, 9, 12, 13 and do exist for all other v equivalent to 0, 1 (mod 4) except, possibly, nu = 17. Much less is known concerning the existence of Z-cyclic triplewhist tournaments. Indeed, there are many open questions related to the existence of Z-cyclic whist designs. A (triple)whist design is said to be Z-cyclic if the players are elements in Z(m) boolean OR A where m = nu, A = 0 when nu equivalent to 1 (mod 4) and m = nu-1, A = {infinity} when nu equivalent to 0 (mod 4) and it is further required that the rounds also be cyclic in the sense that the rounds can be labelled, say, R(1), R(2),... in such a way that R(j+1) is obtained by adding +1 (mod m) to every element in R(j). The production of Z-cyclic triplewhist designs is particularly challenging when m is divisible by any of 5, 9, 11, 13, 17. Here we introduce several new triplewhist frames and use them to construct new infinite families of triplewhist designs, many for the case of m being divisible by at least one of 5, 9, 11, 13, 17.

• 出版日期2006-7-15
• 单位浙江大学