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Z-cyclic triplewhist tournaments—The noncompatible case, part I

✍ Scribed by Norman J. Finizio

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
172 KB
Volume
5
Category
Article
ISSN
1063-8539

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✦ Synopsis

Two odd primes

For all noncompatible (ordered) pairs of primes (p 1 , p 2 ) such that p i ≡ 1 (mod 4), p i < 200, i = 1, 2 we establish the existence of Z-cyclic triplewhist tournaments on 3p 1 p 2 +1 players. It is believed that these results are the first examples of such tournaments, indeed the first examples of Z-cyclic whist tournaments for such players. In Part 2 we extend the results of this study and establish the existence of Z-cyclic triplewhist tournaments on 3p α 1 1 p α 2 2 + 1 players for all α 1 ≥ 1, α 2 ≥ 1 and p 1 , p 2 as described above.

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Z-cyclic triplewhist tournaments—The non
Z-cyclic triplewhist tournaments—The noncompatible case, part II
✍ Norman J. Finizio 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 191 KB

Two odd primes p1 = 2 b 1 u1 + 1, p2 = 2 b 2 u2 + 1, u1 , u2 odd, are said to be noncompatible if b1 / = b2 . Let bi ≥ 2, i = 1, 2 and denote the set {(p1 , p2 ): {p1 , p2 } are noncompatible, pi < 200} by NC. In Part 1 of this study we established the existence of Z-cyclic triplewhist tournaments o

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✍ Norman J. Finizio 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 503 KB

When the number of players, v, in a whist tournament, Wh(v), is = 1 (mod 4) the only instances of a 2-cyclic triplewhist tournament, TWh(v), that appear in the literature are for v = 21,29,37. In this study we present 2-cyclic TWh(v) for all v E T = {v = 8u + 5: v is prime, 3 5 u 5 249). Additionall