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Z-cyclic generalized whist frames and Z-cyclic generalized whist tournaments

โœ Scribed by Norman J Finizio; Brian J Travers


Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
217 KB
Volume
279
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


Much of the work in this article was inspired by the elegant and powerful method introduced by Ge and Zhu in their recent paper on triplewhist frames. We extend their ideas to generalized whist tournament designs. Thus, in one sense, we provide a complete generalization of their methodology. We also incorporate the product theorems of Anderson et al. to broaden their class of Z-cyclic frames. Our techniques are illustrated by the production of many new Z-cyclic (2,6) GWhD(v) that would be di cult to produce by any other existing method.


๐Ÿ“œ SIMILAR VOLUMES


Construction of Z-cyclic triple whist to
โœ Y. S. Liaw ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 735 KB

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 prime

A representation theorem and Z-cyclic wh
โœ Norman J. Finizio ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 538 KB

Let E denote the group of units (i.e., the reduce set of residues) in the ring Z3p,,n. Here we consider q,p to be primes, q = 3 (mod 4), q 2 7, p = 1 (mod 4). Let W denote a common primitive root of 3, q, and p 2 . If H denotes the (normal) subgroup of E that is generated by {-1, W } , we show that

New Product Theorems for Z-Cyclic Whist
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.

Cyclically resolvable designs and triple
โœ I. Anderson; N. J. Finizio ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 552 KB

## We construct cyclically resolvable (v, 4 , l ) designs and cyclic triple whist tournaments Twh(v) for all v of the form 3pt'. . .p> + 1, where the pi are primes 3 1 (mod 4), such that each p1 -1 is divisible by the same power of 2.