Counting Orbifolds
Abstract
We present several methods of counting the orbifolds CD/Gamma. A correspondence between counting orbifold actions on CD, brane tilings, and toric diagrams in D-1 dimensions is drawn. Barycentric coordinates and scaling mechanisms are introduced to characterize lattice simplices as toric diagrams. We count orbifolds of C3, C4, C5, C6 and C7. Some remarks are made on closed form formulas for the partition function that counts distinct orbifold actions.
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