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Colourings of lattices and coincidence site lattices
Colourings of lattices coincidence site lattices
2010/11/9
The relationship between the coincidence indices of a lattice $\Gamma_1$ and a sublattice $\Gamma_2$ of $\Gamma_1$ is examined via the colouring of $\Gamma_1$ that is obtained by assigning a unique c...
Lattices and Parameter Reduction in Division Algebras
Lattices Parameter Reduction Division Algebras
2010/10/29
Let k be an algebraically closed field of characteristic 0 and let D be a division algebra whose center F contains k. We shall say that D can be reduced to r parameters if D = D_0 tensor_{F_0} F, whe...
Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces
Trees Hypercubic Lattices Non-orientable Surfaces
2010/11/2
We consider the problem of enumerating spanning trees on lattices. Closed-form expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N_1 x N_2 x...x N_d ...