Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T06:29:21.232Z Has data issue: false hasContentIssue false
  • English
  • Français

Some sign properties of symmetric functions

Published online by Cambridge University Press:  24 October 2008

D. B. Hunter  and
I. G. Macdonald
D. B. Hunter
Affiliation:
Department of Mathematics, University of Bradford
I. G. Macdonald
Affiliation:
School of Mathematical Sciences, Queen Mary College, London
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Hunter, D. B.. The positive-definiteness of the complete symmetric functions of even order. Math. Proc. Camb. Philos. Soc. 82 (1977), 255–258.CrossRefGoogle Scholar
[2]Jacobson, N., Basic Algebra, vol. 1 (W. H. Freeman & Co., 1974).Google Scholar
[3]Macdonald, I. G., Symmetric Functions and Hall Polynomials (Clarendon Press, 1979).Google Scholar