Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials

  • Manfred Göbel

Abstract.

Any symmetric polynomial fR[X1, …, Xn] has a unique representation f = p1, …, σn) with pR[X1, …, Xn] in the elementary symmetric polynomials σ1, …, σn. This paper investigates higher order symmetric polynomials; these are symmetric polynomials with a representation p, which is also symmetric. We present rewriting techniques for higher order symmetric polynomials and exact degree bounds for the generators of the corresponding invariant rings. Moreover, we point out how algorithms and degree bounds for these polynomials are related to Pascals triangle, Fibonacci numbers, Chebyshev polynomials, and cardinalities of finite distributive lattices of semi-ideals.

Key words: Symmetric polynomials, Higher order symmetry, Degree bounds, Generators, Rewriting techniques 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Manfred Göbel
    • 1
  1. 1.International Computer Science Institute, 1947 Center Street (Suite 600), Berkeley, CA 94704-1198, USAUS

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