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XVI.—On Certain Numerical Coefficients Associated with Partitions
Published online by Cambridge University Press: 14 February 2012
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
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