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
Z-cyclic generalized whist frames and Z-cyclic generalized whist tournaments
โ 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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โฆ 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.
๐ SIMILAR VOLUMES
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.
## 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.