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Construction of Z ‐cyclic triple whist tournaments
Author(s) -
Liaw Y. S.
Publication year - 1996
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1996)4:4<219::aid-jcd1>3.0.co;2-i
Subject(s) - mathematics , prime (order theory) , tournament , integer (computer science) , combinatorics , cyclic group , pi , geometry , computer science , abelian group , programming language
Let p = 2 k t + 1 be a prime where t >1 is an odd integer, k ≥ 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 all primes p,p ≡1(mod 4), 29 ≤ p ≤ 16097, except p = 257. Let p i = 2 k it i + 1, q = 2 k 0t 0 + 3 be primes where t i ; i = 0,1,…, n are odd > 1 and k i are integers ≥2. We prove that if Z ‐cyclic TWh(p i ) and TWh ( q + 1) exist then Z ‐cyclic TWh (∏ n i = 1 p a ii ) and TWh ( q ∏ n i = 1 p a ii + 1) exist. © 1996 John Wiley & Sons, Inc.