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Redfield's Theorems and Multilinear Algebra

Published online by Cambridge University Press:  20 November 2018

Dennis E. White
Dennis E. White*
Affiliation:
University of California, San Diego, La Jolla, California ; University of Minnesota, Minneapolis, Minnesota
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1. Introduction. The remarkable 1927 paper by J. H. Redfield [13] which anticipated many recent combinatorial results in Polya counting theory and, in fact, predated Polya's theorem by ten years has been discussed at length by Harary and Palmer [8], Foulkes [5; 6], Sheehan [15; 16] and Read [12], not to mention de Bruijn [3] and others. We shall, in this paper, demonstrate how multilinear techniques may be used in this context. The Redfield superposition theorem and decomposition theorem turn out to be statements about a group acting on finite function spaces, and may thus be dealt with in multilinear terms. We shall prove Redfield's results and an extension due to Foulkes [5].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 704 - 714
Copyright
Copyright © Canadian Mathematical Society 1975

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