Double Youden rectangles of sizes px(2p+1) and (p+1)x(2p+1)

Preece, D.A. and Vowden, B.J. and Phillips, N.C.K. (1999) Double Youden rectangles of sizes px(2p+1) and (p+1)x(2p+1). Ars Combinatoria, 51 . pp. 161-171. ISSN 0381-7032. (The full text of this publication is not available from this repository)

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Abstract

A k x v double Youden rectangle (DYR) is a type of balanced Graeco-Latin design where each Roman letter occurs exactly once in each of the Ic rows, where each Greek letter occurs exactly once in each of the v columns, and where each Roman letter is paired exactly once with each Creek Better. The other properties of a DYR are of balance, and indeed the structure of a DYR incorporates that of a symmetric balanced incomplete block design (SBIBD). Few general methods of construction of DYRs are known, and these cover only some of the sizes k x v with k = p (odd) or p + 1, and v = 2p + 1. Computer searches have however produced DYRs for those such sizes, p less than or equal to 11, for which the existence of a DYR was previously in doubt. The new DYRs have cyclic structures. A consolidated table of DYRs of sizes p x (2p + 1) and (p + 1) x (2p + 1) is provided for p less than or equal to 11; for each of several of the sies, DYRs are given for different inherent SBIBDs.

Item Type: Article
Subjects: Q Science
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: 22 Apr 2009 17:54
Last Modified: 22 Apr 2009 17:54
Resource URI: http://kar.kent.ac.uk/id/eprint/16492 (The current URI for this page, for reference purposes)
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