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
Inductive extensions of some Z-cyclic whist tournaments
โ Scribed by Norman J. Finizio; Philip A. Leonard
- Book ID
- 108316469
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 430 KB
- Volume
- 197-198
- Category
- Article
- ISSN
- 0012-365X
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๐ SIMILAR VOLUMES
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
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
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.