On the completion of Latin rectangles to symmetric Latin squares

Bryant, D. and Rodger, C. A. (2004) On the completion of Latin rectangles to symmetric Latin squares. Journal of The Australian Mathematical Society, 76 1: 109-124. doi:10.1017/S1446788700008739


Author Bryant, D.
Rodger, C. A.
Title On the completion of Latin rectangles to symmetric Latin squares
Journal name Journal of The Australian Mathematical Society   Check publisher's open access policy
ISSN 1446-7887
Publication date 2004-01-01
Sub-type Article (original research)
DOI 10.1017/S1446788700008739
Volume 76
Issue 1
Start page 109
End page 124
Total pages 16
Editor C. Miller
Place of publication Australia
Publisher Australian Mathematical Society
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract 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 K-n (n even), and for an n-edge colouring of K-n (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.
Keyword Mathematics
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 12:59:14 EST