Vowden, B.J. and Preece, D.A. (1999) Some new infinite series of Freeman-Youden rectangles. Ars Combinatoria, 51 . pp. 49-63. ISSN 0381-7032.
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A Freeman-Youden rectangle (FYR) is a Graeco-Latin row-column design consisting of a balanced superimposition of two Youden squares. There are well known infinite series of FYRs of size q x (2q + 1) and (q + 1) x (2q + 1) where 2q + 1 is a prime power congruent to 3 (modulo 4). However, Preece and Cameron  additionally gave a single FYR of size 7 x 15. This isolated example is now shown to belong to one of a set of infinite series of FYRs of size q x (2q + 1) where q, but not necessarily 2q +1, is a prime power congruent to 3 (modulo 4), q > 3; there are associated series of FYRs of size (q + 1) x (2q + 1). Both the old and the new methodologies provide FYRs of sizes 9 x (2q + 1) and (q + 1) x (2q + 1) where both q and 2q + 1 are congruent to 3 (modulo 4), q > 3; we give special attention to the smallest such size, namely 11 x 23.
|Subjects:||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:||18 Mar 2009 12:43|
|Last Modified:||18 Mar 2009 17:34|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/16717 (The current URI for this page, for reference purposes)|
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