Partitioning 3-homogeneous latin bitrades

Hamalainen, Carlo (2008) Partitioning 3-homogeneous latin bitrades. Geometriae Dedicata, 133 1: 181-193. doi:10.1007/s10711-008-9242-4


Author Hamalainen, Carlo
Title Partitioning 3-homogeneous latin bitrades
Journal name Geometriae Dedicata   Check publisher's open access policy
ISSN 0046-5755
1572-9168
Publication date 2008-04
Sub-type Article (original research)
DOI 10.1007/s10711-008-9242-4
Volume 133
Issue 1
Start page 181
End page 193
Total pages 13
Place of publication Dordrecht, Netherlands
Publisher Springer Netherlands
Language eng
Formatted abstract
A latin bitrade (T, T) is a pair of partial latin squares that define the difference between two arbitrary latin squares LT and L ⊇ T ) of the same order. A 3-homogeneous bitrade (T , T) has three entries in each row, three entries in each column, and each symbol appears three times in T . Cavenagh [2] showed that any 3-homogeneous bitrade may be partitioned into three transversals. In this paper we provide an independent proof of Cavenagh's result using geometric methods. In doing so we provide a framework for studying bitrades as tessellations in spherical, euclidean or hyperbolic space. Additionally, we show how latin bitrades are related to finite representations of certain triangle groups.
Keyword Latin square
Latin bitrade
Triangle group
Tessellation
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Thu, 03 Sep 2009, 10:17:38 EST by Mr Andrew Martlew on behalf of Mathematics