Existence of whist tournaments with the three-person property 3PWh(v)

Lu, Y.; Zhang, Shengyuan

doi:10.1016/s0166-218x(99)00195-x

Cited by 8 publications

(22 citation statements)

References 7 publications

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“…(18,10,19,26), (7,16,31,12), (21,20,27,9), (15,25,28,11), (1,13,29,23), (24,22,3,14), (30,17,4,32). 45 (1,3,5,21), (4,43,6,34), (33,41,14,29), (7,25,32,10), (44,12,31,28), (13,17,8,18), (22,2,…”

Section: Direct Constructionsmentioning

confidence: 99%

“…45 (1,3,5,21), (4,43,6,34), (33,41,14,29), (7,25,32,10), (44,12,31,28), (13,17,8,18), (22,2,15,39), (40,9,19,26), (38,37,16,27), (35,30,24,36), (20,11,23,42). 49 (42, 40, 39, 24), (27,48,44,3), (23,45,10,16), (46,37,28,…”

Section: Direct Constructionsmentioning

confidence: 99%

“…11 (3,39,36,37), (2,26,18,14), (3,26,4,17), (4,43,17,46), (1,7,8,54), (2,46,53,19), (4,42,48,36), (3,36,17,19), (2,9,36,33), (2,43,34,6), (1,38,27,19). (0, 19, 2, 1), (6,37,9,33), (16,18,22,19), (29,2,13,…”

Section: Direct Constructionsmentioning

confidence: 99%

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Ordered tournaments and ordered triplewhist tournaments with the three person property

Abel

2008

J of Combinatorial Designs

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Section: Direct Constructionsmentioning

confidence: 99%

Section: Direct Constructionsmentioning

confidence: 99%

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Ordered tournaments and ordered triplewhist tournaments with the three person property

Abel

2008

J of Combinatorial Designs

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“…The following construction comes from Ref. [20], which is an analogous one of Baker to construct TWhð4nÞs from certain SOLSSOMðnÞs in Ref. [4].…”

Section: Recursive Constructionsmentioning

confidence: 99%

Super‐simple resolvable balanced incomplete block designs with block size 4 and index 3

Lam

2003

J of Combinatorial Designs

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“…A whist tournament is said to have three person-property, denoted by 3PWh(v) as in [19,26,33], if any two games do not have three common players. It was Hartman who first discussed this property in [30].…”

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confidence: 99%

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

Zhang

2007

Des. Codes Cryptogr.

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A directed triplewhist tournament on p players over Z p is said to have the three-person property if no two games in the tournament have three common players. We briefly denote such a design as a 3PDTWh( p). In this paper, we investigate the existence of a Z-cyclic 3PDTWh( p) for any prime p ≡ 1 (mod 4) and show that such a design exists whenever p ≡ 5, 9, 13 (mod 16) and p ≥ 29. This result is obtained by applying Weil's theorem. In addition, we also prove that a Z-cyclic 3PDTWh( p) exists whenever p ≡ 1 (mod 16) and p < 10,000 except possibly for p = 257,769.

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Existence of whist tournaments with the three-person property 3PWh(v)

Cited by 8 publications

References 7 publications

Ordered tournaments and ordered triplewhist tournaments with the three person property

Ordered tournaments and ordered triplewhist tournaments with the three person property

Super‐simple resolvable balanced incomplete block designs with block size 4 and index 3

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

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