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Some sign properties of symmetric functions
Published online by Cambridge University Press: 24 October 2008
Abstract
This paper is concerned with the sign properties of the S-functions sλ for real arguments. We show first that sλ is indefinite if any part of the partition λ is odd. Thus it is only if all parts of λ are even that sλ can possibly be positive definite or semi-definite. In this case we show that sλ(x) is positive provided that at least l(λ) of the components of x are non-zero, where l(λ) is the number of parts of the partition λ.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 193 - 196
- Copyright
- Copyright © Cambridge Philosophical Society 1989