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Existence of Z-cyclic 3PTWh (p) for any Prime p≡ 1 (mod 4)

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Abstract

We show that a Z-cyclic triplewhist tournament on p players with three-person property, briefly 3PTWh(p), exists for any prime p≡ 1 (mod 4) with the only exceptions of p=5,13,17.

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References

  1. R. J. R. Abel, N. J. Finizio, G. Ge and M. Greig, New Z-cyclic triplewhist frames and triplewhist tournament designs, preprint.

  2. R. J. R. Abel and G. Ge, Some difference matrix constructions and an almost completion for the existence of triplewhist tournaments TWh(v), European J. Combin., in press.

  3. I. Anderson N. J. Finizio P. Leonard (1999) ArticleTitleNew product theorems for Z-cyclic whist tournaments J. Combin. Theory Ser. A 88 162–166 Occurrence Handle10.1006/jcta.1999.2969 Occurrence Handle2000e:05035

    Article  MathSciNet  Google Scholar 

  4. M. Buratti (2000) ArticleTitleExistence of Z-cyclic triplewhist tournaments for a prime number of players J. Combin. Theory Ser. A 90 315–325 Occurrence Handle0960.05016 Occurrence Handle2001f:05038

    MATH  MathSciNet  Google Scholar 

  5. Y. Chang L. Ji (2004) ArticleTitleOptimal (4up, 5, 1) optical orthogonal codes J. Combin. Des. 5 346–361 Occurrence Handle2005g:05027

    MathSciNet  Google Scholar 

  6. N.J. Finizio (1995) ArticleTitleZ-cyclic triplewhist tournaments–the noncompatible case, Part 1 J. Combin. Des. 3 135–146 Occurrence Handle0886.05022 Occurrence Handle95m:05061

    MATH  MathSciNet  Google Scholar 

  7. N. J. Finizio (1997) ArticleTitleZ-cyclic triplewhist tournaments–the noncompatible case, Part 2 J. Combin. Des. 5 189–201 Occurrence Handle0911.05010 Occurrence Handle98b:05028

    MATH  MathSciNet  Google Scholar 

  8. G. Ge C. W. H. Lam (2003) ArticleTitleSome new triplewhist tournaments TWh(v) J. Combin. Theory, Series A 101 153–159 Occurrence Handle2003j:05034

    MathSciNet  Google Scholar 

  9. G. Ge A. C. H. Ling (2003) ArticleTitleA new construction for Z-cyclic whist tournaments Discrete Appl. Math. 131 643–650 Occurrence Handle10.1016/S0166-218X(03)00381-0 Occurrence Handle2004h:05028

    Article  MathSciNet  Google Scholar 

  10. G. Ge L. Zhu (2001) ArticleTitleFrame constructions for Z-cyclic triplewhist tournaments Bull. Inst. Combin. Appl. 32 53–62 Occurrence Handle2002a:05058

    MathSciNet  Google Scholar 

  11. H. Haanpää P. Kaski (2005) ArticleTitleThe near resolvable 2-(13,4,3) designs and thirteen-player whist tournaments Des. Codes Crypt. 35 271–285 Occurrence Handle10.1007/s10623-003-6738-7

    Article  Google Scholar 

  12. H. Haanpää P. R. J. Östergård (2003) ArticleTitleClassification of whist tournaments with up to 12 players Discrete Appl. Math. 129 399–407 Occurrence Handle2004f:05023

    MathSciNet  Google Scholar 

  13. Y. S. Liaw (1996) ArticleTitleConstruction of Z-cyclic triplewhist tounaments J. Combin. Des. 4 219–233 Occurrence Handle10.1002/(SICI)1520-6610(1996)4:4<219::AID-JCD1>3.0.CO;2-I Occurrence Handle0911.05011 Occurrence Handle97c:05040

    Article  MATH  MathSciNet  Google Scholar 

  14. Y. Lu L. Zhu (1997) ArticleTitleOn the existence of triplewhist tournaments TWh(v) J. Combin. Des. 5 249–256 Occurrence Handle10.1002/(SICI)1520-6610(1997)5:4<249::AID-JCD2>3.0.CO;2-F Occurrence Handle98f:05037

    Article  MathSciNet  Google Scholar 

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Correspondence to Yanxun Chang.

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Communicated by: J. D. Key

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Feng, T., Chang, Y. Existence of Z-cyclic 3PTWh (p) for any Prime p≡ 1 (mod 4). Des Codes Crypt 39, 39–49 (2006). https://doi.org/10.1007/s10623-005-2327-2

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  • DOI: https://doi.org/10.1007/s10623-005-2327-2

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