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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: 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].


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

  • [1] 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.
  • [2] L. Flatto, Basic sets of invariants for finite reflection groups, Bull. Amer. Math. Soc. 74 (1968), 730-734. MR 37 #1483. MR 0225892 (37:1483)
  • [3] T. J. L. Bromwich, An introduction to the theory of infinite series, 2nd ed., Macmillan, London, 1926.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0257042-X
Keywords: Algebraic independence, symmetric polynomials, roots of unity
Article copyright: © Copyright 1970 American Mathematical Society

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