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Partition functions for non-interacting particles are known to be symmetricfunctions. It is shown that powerful group-theoretical techniques can be usednot only to derive these relationships, but also to significantly simplifycalculation of the partition functions for particles that carry internalquantum numbers. The partition function is shown to be a sum of one or moregroup characters. The utility of character expansions in calculating thepartition functions is explored. Several examples are given to illustrate thesetechniques.Comment: 16 pages of RevTe

Partition functions in statistical mechanics, symmetric functions, and group representations