(3,6) GWhD(v): existence results

  • Authors:

  • R. J. R. Abel;Norman J. Finizio;Malcolm Greig

  • Affiliations:

  • School of Mathematics, University of New South Wales, Sydney 2052, Australia;Department of Mathematics, University of Rhode Island, Kingston, RI;Greig Consulting, 317-130 East 11th Street, North Vancouver, B.C., Canada V7L 4R3

  • Venue:
  • Discrete Mathematics - Papers on the occasion of the 65th birthday of Alex Rosa
  • Year:
  • 2003

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Abstract

Necessary conditions for the existence of (3,6) generalized Whist tournament designs on υ players are that υ ≡ 0, 1 (mod 6). For υ = 6n + 1 it is shown that these designs exist for all n. For υ = 6n, it is impossible to have a design for n = 1, but for n 1 it is shown that designs exist, except possibly for 73 values of n the largest of which is n = 199. A solution is also provided for the only unknown (υ, 6, 5) RBIBD, namely, υ = 174.