Preece, Donald A.
(1994)
*
Triple youden rectangles - a new class of fully balanced combinatorial arrangements.
*
Ars Combinatoria,
37
.
pp. 175-182.
ISSN 0381-7032.
(The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
(KAR id:19959)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. |

## Abstract

Triple Youden rectangles are defined and examples are given. These combinatorial arrangements constitute a special class of k x v row-and-column designs, k < v, with superimposed treatments from three sets, namely a single set of v treatments and two sets of k treatments. The structure of each of these row-and-column designs incorporates that of a symmetrical balanced incomplete block design with v treatments in blocks of size k. Indeed, when either of the two sets of k treatments is deleted from a k x v triple Youden rectangle, a k x v double Youden rectangle is obtained; when both are deleted, a k x v Youden square remains. The paper obtains an infinite class of triple Youden rectangles of size k x (k + 1). Then it presents a 4 x 13 triple Youden rectangle which provides a balanced layout for two packs of playing-cards, and a 7 x 15 triple Youden rectangle which incorporates a particularly remarkable 7 x 15 Youden square. Triple Youden rectangles are fully balanced in a statistical as well as a combinatorial sense, and those discovered so far are statistically very efficient.

Item Type: | Article |
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Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | O.O. Odanye |

Date Deposited: | 10 Jun 2009 08:28 UTC |

Last Modified: | 16 Nov 2021 09:58 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/19959 (The current URI for this page, for reference purposes) |

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