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Abel, R. Julian R.; Bennett, F. E.; Ge, Gennian

doi:10.1016/j.dam.2007.10.027

Discrete Applied Mathematics

2008

DOI: 10.1016/j.dam.2007.10.027

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Existence of directed triplewhist tournaments with the three person property 3PDTWh(v)

R. Julian R. Abel

F. E. Bennett

Gennian Ge

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Cited by 3 publications

References 18 publications

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Decomposable super‐simple NRBIBDs with block size 4 and index 6

Sun

et al. 2018

J of Combinatorial Designs

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Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ( v , 4 , 6 )‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ( v , 4 , 3 )‐BIBDs are v ≡ 1 (mod 4) and v ≥ 17. In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ( v , 4 , 3 )‐RBIBD, namely v ≡ 1 (mod 4) and v ≥ 9, are sufficient. A few new pairwise balanced designs are also given.

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Decomposable super‐simple NRBIBDs with block size 4 and index 6

Sun

et al. 2018

J of Combinatorial Designs

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Partitionable sets, almost partitionable sets, and their applications

Chang

Costa

Feng

et al. 2020

J of Combinatorial Designs

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This paper introduces almost partitionable sets (APSs) to generalize the known concept of partitionable sets. These notions provide a unified frame to construct double-struckZ‐cyclic patterned starter whist tournaments and cyclic balanced sampling plans excluding contiguous units. The existences of partitionable sets and APSs are investigated. As an application, a large number of optical orthogonal codes achieving the Johnson bound or the Johnson bound minus one are constructed.

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General frame constructions for Z-cyclic triplewhist tournaments

2007

Journal of Combinatorial Theory, Series A

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Frames are useful in dealing with resolvable designs such as resolvable balanced incomplete block designs and triplewhist tournaments. Z-cyclic triplewhist tournament frames are also useful in the constructions of Z-cyclic triplewhist tournaments. In this paper, the concept of an (h 1 , h 2 , . . . , h n ; u)-regular Z-cyclic triplewhist tournament frame is defined, and used to establish several quite general recursive constructions for Z-cyclic triplewhist tournaments. As corollaries, we are able to unify many known constructions for Z-cyclic triplewhist tournaments. As an application, some new Z-cyclic triplewhist tournament frames and Z-cyclic triplewhist tournaments are obtained. The known existence results of such designs are then extended.

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Existence of directed triplewhist tournaments with the three person property 3PDTWh(v)

Cited by 3 publications

References 18 publications

Decomposable super‐simple NRBIBDs with block size 4 and index 6

Decomposable super‐simple NRBIBDs with block size 4 and index 6

Partitionable sets, almost partitionable sets, and their applications

General frame constructions for Z-cyclic triplewhist tournaments

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