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Redfield's Theorems and Multilinear Algebra
- Source :
- Canadian Journal of Mathematics. 27:704-714
- Publication Year :
- 1975
- Publisher :
- Canadian Mathematical Society, 1975.
-
Abstract
- 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].
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 27
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........f1f9c1e6bc618aabdce8eb4af019ebf4