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Latin trades in groups defined on planar triangulations

Cavenagh, Nicholas J; Wanless, Ian

Description

For a finite triangulation of the plane with faces properly coloured white and black, let AW be the abelian group constructed by labelling the vertices with commuting indeterminates and adding relations which say that the labels around each white triangle add to the identity. We show that A W has free rank exactly two. Let AW* be the torsion subgroup of AW, and AB* the corresponding group for the black triangles. We show that AW* and AB* have the same order, and conjecture that they are...[Show more]

CollectionsANU Research Publications
Date published: 2009
Type: Journal article
URI: http://hdl.handle.net/1885/20655
Source: Journal of Algebraic Combinatorics
DOI: 10.1007/s10801-008-0165-9

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