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A new formula for cumulants - Corrigenda

Published online by Cambridge University Press:  24 October 2008

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I. J. GOOD. ‘A new formula for cumulants.’

Henryk Minc has pointed out in correspondence that Equation (12), which was a corollary of Theorem 2, does not agree with the computed values of Schur's matrix ω(rs) given by Graham and Lehmer (1976). In the course of the ‘proof’ I made the error of assuming that , overlooking that s could be a multiple of m, so that the sum can also equal m. Since this was the only error, the statement of Theorem 2 is correct modulo m. In particular it shows that perm(ωrs) ≡ 0 (mod m) but this result is much weaker than the results obtained by Graham and Lehmer.

Theorem 1 is unaffected by this error, and moreover has since been proved again by Groeneveld and van Kampen (1977).

Type
Corrigenda
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 2 , March 1982 , pp. 343
Copyright
Copyright © Cambridge Philosophical Society 1982

References

REFERENCES

Good, I. J. (1977). A new formula for k–statistics. Annals of Statistics 5, 224–228.CrossRefGoogle Scholar
Graham, R. L. and Lehmer, D. H. (1976). On the permanent of Schur's matrix. J. Austral. Math. Soc. 21 (Series A), 487–497.CrossRefGoogle Scholar
Groeneveld, J. and Van Kampen, N. G. (1977). A simple proof of an identity of Good. Math. Proc. Cambridge Philos. Soc. 81, 183–184.CrossRefGoogle Scholar