The Near Resolvable 2-(13, 4, 3) Designs and Thirteen-Player Whist Tournaments
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A ν-player whist tournament is a schedule of games, where in each round the ν players are partitioned into games of four players each with at most one player left over. In each game two of the players play as partners against the other two. All pairs of players must play in the same game exactly three times during the tournament; of those three times, they are to play as partners exactly once. Whist tournaments for ν players are known to exist for all ν ≡ 0,1 (mod 4). The special cases of directed whist tournaments and triplewhist tournaments are known to exist for all sufficiently large ν, but for small ν several open cases remain. In this paper we introduce a correspondence between near resolvable 2-(ν, k, λ designs and a particular class of codes. The near resolvable 2-(13, 4, 3) designs are classified by classifying the corresponding codes with an orderly algorithm. Finally, the thirteen-player whist tournaments are enumerated starting from the near resolvable 2-(13, 4, 3) designs.
Keywordsnear resolvable design whist tournament orderly algorithm
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- Anderson, I 1996Whist tournamentsColbourn, CJDinitz, JH eds. The CRC Handbook of Combinatorial DesignsCRC PressBoca Raton504508Google Scholar
- Baker, R. 1975Whist tournamentsCongressus Numerautium1489100Google Scholar
- I. A. Faradžev, Constructive enumeration of combinatorial objects, Colloq Internat CNRS, 260, CNRS, Paris (1978) pp. 131–135.Google Scholar
- The GAP Group, GAP –- Groups, Algorithms, and Programming, Version 4.3; 2002. (http://www.gap-system.org).Google Scholar
- Gibbons, PB 1996Computational methods in design theoryColbourn, CJDinitz, JH eds. The CRC Handbook of Combinatorial DesignsCRC PressBoca Raton718740Google Scholar
- R. Mathon and A. Rosa, 2-(υ, k, λ) designs of small order, In C. J. Colbourn and J. H. Dinitz, CRC Press, Boca Raton (1996) pp. 3–41.Google Scholar
- B. D. McKay, autoson – a distributed batch system for UNIX workstation networks (version 1.3), Technical Report TR-CS-96-03, Computer Science Department, Australian National University (1996).Google Scholar
- B. D. McKay, nauty user’s guide (version 1.5). Technical Report TR-CS-90-02, Computer Science Department, Australian National University (1990).Google Scholar
- N.V. Semakov and V.A. Zinov’ev, Equidistant q-ary codes with maximal distance and resolvable balanced incomplete block designs, Problems of Information Transmission, Vol. 4, No. 2 (1968) pp. 1--7; translated from Problemy Peredachi Informatsii , Vol. 4, No. 2 (1968) pp. 3--10 (Russian). Google Scholar
- T. Syrjänen and I. Niemelä, The Smodels system, In T. Eiter, W. Faber, M. Truszczyński, (eds.), Logic Programming and Nonmonotonic Reasoning: Proc. 6th International Conference, LPNMR 2001, Lecture Notes in Artificial Intelligence, Springer, Berlin, 2173 (2001) pp. 434–438.Google Scholar