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On Redfield's Range-Correspondences

Published online by Cambridge University Press:  20 November 2018

H. O. Foulkes
H. O. Foulkes*
Affiliation:
University College, Swansea, Great Britain
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In an important paper (7), long overlooked, J. H. Redfield dealt with several aspects of enumerative combinatorial analysis. In a previous paper (1) I showed the relation between a certain repeated scalar product of a set of permutation characters of a symmetric group and Redfield's composition of his group reduction functions. Here I consider, from a group representational point of view, Redfield's idea of a range-correspondence and its application to enumeration of linear graphs. The details of the application of these ideas to more general enumerations are also given.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1060 - 1071
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Foulkes, H. O., On Redfield's group reduction functions, Can. J. Math., 15 (1963), 272–284.Google Scholar
2. Hall, M. Jr., Theory oj groups (New York, 1959).Google Scholar
3. Harary, F., The number of linear, directed, rooted and connected graphs, Trans. Amer. Math. Soc., 78 (1955), 445–463.Google Scholar
4. Littlewood, D. E., The theory of group characters and matrix representations of groups, 2nd ed. (Oxford, 1950).Google Scholar
5. Pólya, G., Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math., 68 (1937), 145–254.Google Scholar
6. Read, R. C., The enumeration of locally restricted graphs, J. London Math. Soc, 34 (1959), 417–436.Google Scholar
7. Redfield, J. H., The theory of group reduced distributions, Amer. J. Math., 49 (1927), 433–455.Google Scholar
8. Riordan, J., An introduction to combinatorial analysis (New York, 1958).Google Scholar
9. Uhlenbeck, G. E. and Ford, G. W., Studies in statistical mechanics I, edited by De Boer and Uhlenbeck (Amsterdam, 1962), Part B.Google Scholar