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On the completion of latin rectangles to symmetric latin squares

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Darryn Bryant  and
C. A. Rodger
Darryn Bryant
Affiliation:
Department of Mathematics, University of QueenslandQld 4072, Australia, e-mail: db@mahs.uq.edu.au
C. A. Rodger
Affiliation:
School of Mathematical and Physical Sciences, University of NewcastleNSW 2308, Australia, e-mail: rodgec1@auburn.edu
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Abstract

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We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n−1)-edge colouring of Kn (n even), and for n-edge colouring of Kn (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.

MSC classification

Secondary: 05B15: Orthogonal arrays, Latin squares, Room squares
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 109 - 124
Copyright
Copyright © Australian Mathematical Society 2004

References

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