Rees, D.H.
(1999)
*
Some new generalised Kirkman systems.
*
Utilitas Mathematica, 56
.
pp. 177-199.
ISSN 0315-3681.
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## Abstract

Constructions are given for some generalised Kirkman designs and other perfect Graeco-Latin balanced incomplete block designs. In these designs, each of two sets of treatments is at-ranged with respect to the blocks as a balanced incomplete block design (BIBD) with parameters (v, b, r, k, lambda), each treatment set is arranged with respect to the other as in a symmetric BIBD with parameters (v, v, r, r, mu), and there is adjusted orthogonality between the two sets. Resolvable designs with v = s(3)+s(2)+s+1 and lambda = 1 are constructed from PG(3,s) for s = 2,3,4 and 8, and a further design is constructed from PG(5,2). Resolvable designs with v = 3(s), k = 3 and lambda = 1 are constructed for s = 3 and 5. Relationships with self-orthogonal Latin squares and tournament designs are discussed.

Item Type: | Article |
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Uncontrolled keywords: | balanced incomplete block designs; generalised Kirkman systems; Kirkman designs; row-and-column designs; self-orthogonal Latin squares; spouse-avoiding mixed doubles round robin; designs; perfect Graeco-Latin balanced incomplete block designs |

Subjects: | Q Science Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | F.D. Zabet |

Date Deposited: | 17 Apr 2009 11:03 |

Last Modified: | 17 Apr 2009 11:06 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/16531 (The current URI for this page, for reference purposes) |

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