On the algebraic independence of symmetric functions
Author:
G. K. Haeuslein
Journal:
Proc. Amer. Math. Soc. 25 (1970), 179-182
MSC:
Primary 12.30; Secondary 20.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257042-X
MathSciNet review:
0257042
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Abstract | References | Similar Articles | Additional Information
Abstract: The purpose of this note is to establish a necessary and sufficient condition for the algebraic independence of certain sets of homogeneous symmetric polynomials which is used in 2. to solve a problem proposed by L. Flatto [2].
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A. Cauchy, Mémoire sur diverses formules relatives à l’algèbre et à la théorie des nombres, C. R. Acad. Sci. Paris 12 (1841), 698-711.
- Leopold Flatto, Basic sets of invariants for finite reflection groups, Bull. Amer. Math. Soc. 74 (1968), 730–734. MR 225892, DOI https://doi.org/10.1090/S0002-9904-1968-12017-8 T. J. L. Bromwich, An introduction to the theory of infinite series, 2nd ed., Macmillan, London, 1926.
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Additional Information
Keywords:
Algebraic independence,
symmetric polynomials,
roots of unity
Article copyright:
© Copyright 1970
American Mathematical Society