Ordered tournaments and ordered triplewhist tournaments with the three person property

Abel, R. Julian R.; Ge, Gennian

doi:10.1002/jcd.20185

Cited by 4 publications

(13 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When ∞ is present then ∞ + 1 = ∞. For the existence of Z-cyclic whist tournaments, much less is known despite of the efforts of many authors, such as Abel et al [1,2], Anderson et al [5][6][7], Buratti [12], Feng and Chang [18], Finizio [20,21], Ge and Ling [27], Ge and Zhu [28], and Liaw [31]. The following results are known.…”

Section: Theorem 14 ([23])mentioning

confidence: 91%

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

Zhang

2007

Des. Codes Cryptogr.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Theorem 14 ([23])mentioning

confidence: 91%

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

Zhang

2007

Des. Codes Cryptogr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…For (4, 6)-frames, the direct construction is similar. (17,4, 3)-NRBIBD. Multiplying by 3 gives another super-simple Z-cyclic (17,4,3)-NRBIBD.…”

Section: Direct Constructionsmentioning

confidence: 99%

“…(17,4, 3)-NRBIBD. Multiplying by 3 gives another super-simple Z-cyclic (17,4,3)-NRBIBD. The union of these two supersimple Z-cyclic (17,4,3)-NRBIBDs forms a 3-decomposable super-simple Z-cyclic ( Proof An initial near parallel class for the first (4,3)-subdesign is obtained by multiplying the blocks given in Table 2 Proof These designs are over Z n 4 .…”

Section: Direct Constructionsmentioning

confidence: 99%

“…The known necessary conditions here turn out to be sufficient. As a result, we are also able to obtain super-simple v ( , 4, 3)-NRBIBDs for the values of v given as unknown in [4].…”

mentioning

confidence: 98%

“…For a v λ ( , 4, )-NRBIBD, we must have λ m = 3 , where ≥ m 1 is an integer. In [4], the existence of super-simple v ( , 4, 3)-NRBIBDs (with a few extra whist properties) was investigated, and solutions were obtained for ≡ v 1 (mod 4),…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Sun

et al. 2018

J of Combinatorial Designs

View full text Add to dashboard Cite

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.

show abstract

Partitionable sets, almost partitionable sets, and their applications

Chang

Costa

Feng

et al. 2020

J of Combinatorial Designs

View full text Add to dashboard Cite

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.

show abstract

Ordered tournaments and ordered triplewhist tournaments with the three person property

Cited by 4 publications

References 26 publications

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

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

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

Partitionable sets, almost partitionable sets, and their applications

Contact Info

Product

Resources

About