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XVI.—On Certain Numerical Coefficients Associated with Partitions

Published online by Cambridge University Press:  14 February 2012

D. E. Rutherford
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Extract

§ 1. The principal object of this note is to establish formula (16) of the preceding paper by H. Jack (1966). This formula, which was conjectured by Jack, evaluates a certain coefficient which is attached to a symbol {p, q, …, r}. In this symbols, p, q, …, r form a partition of m such that o≤p≤q≤…≤r,p+q+…+r=m. The symbol however vanishes if any two of the integers p, q, … r are equal but non-zero. In the remaining cases we have to show that the coefficient in question has the value

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 3 , 1967 , pp. 215 - 219
Copyright
Copyright © Royal Society of Edinburgh 1967

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References

References to Literature

Jack, H., 1966. “A Matrix Analogue of the Integral ”, Proc. Roy. Soc. Edin., A, 67, 205–214.Google Scholar
Rutherford, D. E., 1942. “On the Relations between the Numbers of Standard Tableaux”, Proc. Edin. Math. Soc., 7, 51–54.Google Scholar