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Z‐cyclic triplewhist tournaments—The noncompatible case, part II
Author(s) -
Finizio Norman J.
Publication year - 1997
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(1997)5:3<189::aid-jcd3>3.0.co;2-b
Subject(s) - mathematics , combinatorics , tournament
Two odd primes p 1 = 2 b 1u 1 + 1, p 2 = 2 b 2u 2 + 1, u 1 , u 2 odd, are said to be noncompatible if b 1 ≠ b 2 . Let b i ≥ 2, i = 1, 2 and denote the set {( p 1 , p 2 ): { p 1 , p 2 } are noncompatible, p i < 200} by NC. In Part 1 of this study we established the existence of Z‐cyclic triplewhist tournaments on 3 p 1 p 2 + 1 players for all ( p 1 , p 2 ) ϵ NC . Here we extend these results and establish Z‐cyclic triplewhist tournaments on 3 p 1 α 1p 2 α 2+ 1 players for all ( p 1 , p 2 ) ϵ NC and for all α 1 ≥ 1, α 2 ≥ 1. It is believed that these are the first infinite classes of such triplewhist tournaments. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 189–201, 1997