Vowden, Barry J. and Preece, Donald A.
(1999)
*Some new infinite series of Freeman-Youden rectangles.*
Ars Combinatoria, 51
.
pp. 49-63.
ISSN 0381-7032.
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## Abstract

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 [9] 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.

Item Type: | Article |
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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: | 04 Jun 2014 08:49 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/16717 (The current URI for this page, for reference purposes) |

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