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Proceedings of the American Mathematical Society

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Generalisation of the Muirhead-Rado inequality

Author: D. E. Daykin
Journal: Proc. Amer. Math. Soc. 30 (1971), 84-86
MSC: Primary 26.60
MathSciNet review: 0279255
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Abstract: For polynomials $ {f_\beta }(x)$ of n real variables $ x = ({x_1},{x_2}, \cdots ,{x_n})$ of the form

$\displaystyle {f_\beta }(x) = \sum\limits_i {\sum\limits_j {x_{\rho (i,1)}^{{\b... ...rho (i,2)}^{{\beta _2}{e_{j2}}} \cdots } } x_{\rho (i,n)}^{{\beta _n}{e_{jn}}},$

conditions are given which ensure that $ {f_\alpha }(x) \leqq {f_\beta }(x)$ for all $ x \geqq 0$.

References [Enhancements On Off] (What's this?)

  • [1] T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Springer-Verlag, Berlin-New York, 1974 (German). Berichtigter Reprint. MR 0344997
  • [2] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, New York, 1934.
  • [3] R. F. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters, Proc. Edinburgh Math. Soc. 21 (1903), 144-157.
  • [4] R. Rado, An inequality, J. London Math. Soc. 27 (1952), 1–6. MR 0045168
  • [5] D. E. Daykin, Inequalities for functions of a cyclic nature, J. London Math. Soc. (2) 3 (1971), 453–462. MR 0284394

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Keywords: Convex hull, inequality, Muirhead, permutation group, polynomial, Rado, symmetric function
Article copyright: © Copyright 1971 American Mathematical Society