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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generalisation of the Muirhead-Rado inequality


Author: D. E. Daykin
Journal: Proc. Amer. Math. Soc. 30 (1971), 84-86
MSC: Primary 26.60
DOI: https://doi.org/10.1090/S0002-9939-1971-0279255-4
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$.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0279255-4
Keywords: Convex hull, inequality, Muirhead, permutation group, polynomial, Rado, symmetric function
Article copyright: © Copyright 1971 American Mathematical Society