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2020•Rocky Mountain Journal of MathematicsOpen access

A generalized Newton–Girard formula for monomial symmetric polynomials

Samuel Chamberlin, Azadeh Rafizadeh

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Abstract

The Newton–Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have generalized this identity by replacing the elementary symmetric polynomials with monomial symmetric polynomials. Our formula has an application in the field of Lie algebras.

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The Newton–Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have generalized this identity by replacing the elementary symmetric polynomials with monomial symmetric polynomials. Our formula has an application in the field of Lie algebras.

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Available abstract

The Newton–Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have generalized this identity by replacing the elementary symmetric polynomials with monomial symmetric polynomials. Our formula has an application in the field of Lie algebras.

Key concepts: Power sum symmetric polynomial, Complete homogeneous symmetric polynomial, Elementary symmetric polynomial, Mathematics, Ring of symmetric functions, Monomial, Symmetric polynomial, Stanley symmetric function

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