Skip to main content
Kent Academic Repository

Some new infinite series of Freeman-Youden rectangles

Vowden, Barry J., Preece, Donald A. (1999) Some new infinite series of Freeman-Youden rectangles. Ars Combinatoria, 51 . pp. 49-63. 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:16717)

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

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
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: F.D. Zabet
Date Deposited: 18 Mar 2009 12:43 UTC
Last Modified: 16 Nov 2021 09:54 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/16717 (The current URI for this page, for reference purposes)

University of Kent Author Information

Vowden, Barry J..

Creator's ORCID:
CReDIT Contributor Roles:

Preece, Donald A..

Creator's ORCID:
CReDIT Contributor Roles:
  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.