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A formula for the calculation of the number of Wyckoff sequences of a given length is presented, based on the combinatorics of multisets with finite multiplicities and a generating function approach, assuming a certain space-group type and taking into account the number of non-fixed and fixed Wyckoff positions, respectively. The formula is applied to the 44 distinguishable combinatorial types of the 230 space-group types. A comparison is made between the calculated frequencies of occurrence of Wyckoff sequences of given space-group type and length and the observed ones for actual crystal structures, as retrieved from the Pearson's Crystal Data Crystal Structure Database for Inorganic Compounds.

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Mathematical background, data and plots for the calculated and observed frequencies of occurrence of Wyckoff sequences of given length for all space group types.

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