Preece, D.A and Vowden, B.J
(1995)
*Greco-latin squares with embedded balanced superimpositions of youden squares.*
Discrete Mathematics, 138
(1-3).
pp. 353-363.
ISSN 0012-365X .
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## Abstract

Parker's (1959) first example of a 10 x 10 Graeco-Latin square incorporates 4 balanced superimpositions of 3 x 7 Youden squares. Such superimpositions of size a x (2s + 1), where s is odd and (2s + 1) is prime, can be of two types, distinguished by the values taken by an invariant formed from the incidence matrices for the superimpositions. All four of the superimpositions in Parker's example are of Type 1. We now give 10 x 10 Graeco-Lattin squares similar to Parker's, but with x(= 0, 2, 3) superimpositions of Type 1 and 4 - x of Type 2. Our 10 x 10 examples with x = 0, 2, 3 and 4 are shown to be special cases of constructions for Graeco-Latin squares of order 3s + 1; Graeco-Latin squares with x = 1 are shown to be impossible.

Item Type: | Article |
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Additional information: | Document Type: Proceedings Paper. Conference Information: 14th British Combinatorial Conference/Annual General Meeting of the Institute-of-Combinatorics-and-Its-Applications UNIV KEELE, KEELE, ENGLAND, JUL 05-09, 1993 INST COMBINATORICS & ITS APPLICAT |

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: | 02 Jun 2009 09:19 |

Last Modified: | 02 Jun 2009 09:19 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/19461 (The current URI for this page, for reference purposes) |

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