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On compound permutation matrices

Published online by Cambridge University Press:  20 January 2009

A. C. Aitken
A. C. Aitken
Affiliation:
The Mathematical Institute, The University, Edinburgh, 1.
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In an earlier paper1 the author investigated the relation existing between the induced matrices of a group of permutation matrices and the table of group characters of the irreducible representations of the corresponding symmetric group. It was found that the traces of a particular set of induced matrices sufficed to give, by a relatively simple transformation, the complete table of characters.It was remarked also that for n > 4 the set of compound matrices of permutation matrices, on the other hand, could at most provide only part of the table; for in fact the number of compounds, n + 1. is then less than P (n), the numbe'r of partitions of n. For this reason the subject was not pursued into further detail.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 7 , Issue 4 , October 1946 , pp. 196 - 203
Copyright
Copyright © Edinburgh Mathematical Society 1946

References

page 196 note 1Proc. Edin. Math. Soc. (2), 5 (1937), 1–13.Google Scholar

page 197 note 1Combinatory Analysis, 1916, vol. i, 153.Google Scholar

page 198 note 1 See for example Littlewood, D. E., The Theory of Group Characters, 1940, 63–67.Google Scholar

page 199 note 1MacMahon, , Combinatory Analysis, vol. i, 3–7.Google Scholar

page 199 note 2Ibid., vol. i, 200.

page 201 note 1Proc. London Math. Soc. (2), 38 (1935), 367, 370.Google Scholar

page 201 note 2Proc. London Math. Soc. (2), 40 (1936), 375,Google Scholar or Theory of Group Characters, 198.Google Scholar

page 201 note 3Proc. Roy. Soc, Edin., 56 (1936), 77–78.Google Scholar