# Triangulations of the sphere, bitrades and abelian groups

@article{Blackburn2014TriangulationsOT, title={Triangulations of the sphere, bitrades and abelian groups}, author={Simon R. Blackburn and Thomas A. McCourt}, journal={Combinatorica}, year={2014}, volume={34}, pages={527-546} }

Let $$\mathcal{G}$$ be a triangulation of the sphere with vertex set V, such that the faces of the triangulation are properly coloured black and white. Motivated by applications in the theory of bitrades, Cavenagh and Wanless defined $$\mathcal{A}_W$$ to be the abelian group generated by the set V, with relations r+c+s = 0 for all white triangles with vertices r, c and s. The group $$\mathcal{A}_B$$ can be de fined similarly, using black triangles.The paper shows that $$\mathcal{A}_W$$ and… CONTINUE READING

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