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On Pólya's Theorem

Published online by Cambridge University Press:  20 November 2018

J. Sheehan
J. Sheehan*
Affiliation:
University College of Swansea, and King's College, Aberdeen
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In 1927 J. H. Redfield (9) stressed the intimate interrelationship between the theory of finite groups and combinatorial analysis. With this in mind we consider Pólya's theorem (7) and the Redfield-Read superposition theorem (8, 9) in the context of the theory of permutation representations of finite groups. We show in particular how the Redfield-Read superposition theorem can be deduced as a special case from a simple extension of Pólya's theorem. We give also a generalization of the superposition theorem expressed as the multiple scalar product of certain group characters. In a later paper we shall give some applications of this generalization.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 792 - 799
Copyright
Copyright © Canadian Mathematical Society 1967

References

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