Skip to main content
Log in

Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

Any symmetric polynomial fR[X 1, …, X n] has a unique representation f = p1, …, σn) with pR[X 1, …, X n] 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received: December 16, 1997

Rights and permissions

Reprints and permissions

About this article

Cite this article

Göbel, M. Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials. AAECC 9, 559–573 (1999). https://doi.org/10.1007/s002000050118

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002000050118

Navigation