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- W2058786147 abstract "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 v = 5 , 9 , 12 , 13 and do exist for all other v ≡ 0 , 1 ( mod 4 ) except, possibly, v = 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 ∪ A where m = v , A = ∅ when v ≡ 1 ( mod 4 ) and m = v - 1 , A = { ∞ } when v ≡ 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 ." @default.
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- W2058786147 date "2006-07-01" @default.
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- W2058786147 title "New Z-cyclic triplewhist frames and triplewhist tournament designs" @default.
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- W2058786147 doi "https://doi.org/10.1016/j.dam.2006.03.001" @default.
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