Triple youden rectangles - a new class of fully balanced combinatorial arrangements

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)

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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
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: O.O. Odanye
Date Deposited: 10 Jun 2009 08:28
Last Modified: 04 Jun 2014 08:51
Resource URI: https://kar.kent.ac.uk/id/eprint/19959 (The current URI for this page, for reference purposes)
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