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Coincidence Site Lattices (CSLs) are a well established tool in the theory ofgrain boundaries. For several lattices up to dimension $d=4$, the CSLs areknown explicitly as well as their indices and multiplicity functions. Many ofthem share a particular property: their multiplicity functions aremultiplicative. We show how multiplicativity is connected to certaindecompositions of CSLs and the corresponding coincidence rotations and presentsome criteria for multiplicativity. In general, however, multiplicativity isviolated, while supermultiplicativity still holds.

Multiplicativity in the theory of coincidence site lattices