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A Theorem Concerning Partitions and its Consequence in the Theory of Lie Algebras

Published online by Cambridge University Press:  20 November 2018

J. W. B. Hughes
J. W. B. Hughes*
Affiliation:
Queen Mary College, London
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In the first part of this paper we state and prove a theorem concerning the partition (j; l, i) of an integer j into at most l integers , none of which exceed i; l and i being themselves integers, (j; l, i) is thus the number of distinct solutions of the equations

1.1

where the satisfy the inequalities

1.2

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 698 - 700
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Dickson, L. E., History of the theory of numbers, Vol. 2 (Stechert, New York, 1934).Google Scholar
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3. Dynkin, E. B., Some properties of the system of weights of a linear representation of a semisimple Lie group, Dokl. Akad. NaukSSSR (N.S.), 71 (1950), 221.Google Scholar
4. Hughes, J. W. B., Theory of unitary groups, University College, London, Department of Physics Review paper (September, 1965).Google Scholar