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Construction of Z-cyclic triple whist tournaments

โœ Scribed by Y. S. Liaw

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
735 KB
Volume
4
Category
Article
ISSN
1063-8539

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โœฆ Synopsis

Let p = Z k t + 1 be a prime where t > 1 is an odd integer, k 2 2. Methods of constructing a Z-cyclic triple whist tournament TWh(p) are given. By such methods we construct a Z-cyclic TWh(p) for d l primes p , p = l(mod 4), 29 5 p 5 16097, except p = 257. Let p , = 2ktt, + 1, q = Zk0oto + 3 be primes where t , ; z = 0,1,. . . , n. are odd > 1 and k, are integers 2 2. We prove that if Z-cyclic TWh(p,) and TWh(q + 1) exist then Z-cyclic TWh(n,"=l p p z ) and T W h ( q n r = , pPt + 1) exist.

๐Ÿ“œ SIMILAR VOLUMES

New Product Theorems for Z-Cyclic Whist
New Product Theorems for Z-Cyclic Whist Tournaments
โœ Ian Anderson; Norman J. Finizio; Philip A. Leonard ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 86 KB

The aim of this note is to show how existing product constructions for cyclic and 1-rotational block designs can be adapted to provide a highly effective method of obtaining product theorems for whist tournaments.

Existence of Z-Cyclic Triplewhist Tourna
Existence of Z-Cyclic Triplewhist Tournaments for a Prime Number of Players
โœ Marco Buratti ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 123 KB

A Z-cyclic triplewhist tournament for 4n+1 players, or briefly a TWh(4n+1), is equivalent to a . The existence problem for Z-cyclic TWh( p)'s with p a prime has been solved for p 1 (mod 16). I. Anderson