Abstract
The problem of base changes for the classical symmetric functions has been solved a long time ago and has been incorporated into most computer software packages for symmetric functions. In this paper, we develop a simple recursive formula for the expansion of the augmented monomial symmetric functions into power sum symmetric functions. As corollaries, we present two algorithms that can be used to expressing the augmented monomial symmetric functions in terms of the power sum symmetric functions.
Highlights
Any positive integer n can be written as a sum of one or more positive integers, i.e., n = 1 + 2 + ··· + r. (1)When the order of integers i does not matter, this representation is known as an integer partition Andrews (1976) and can be rewritten as n = t1 + 2t2 + · · · + ntn where each positive integer i appears ti times
We develop a simple recursive formula for the expansion of the augmented monomial symmetric functions into power sum symmetric functions
We present two algorithms that can be used to expressing the augmented monomial symmetric functions in terms of the power sum symmetric functions
Summary
The power sum symmetric functions pk do not have enough elements to form a basis for kn, there must be one function for every partition ⊢ k. We present two algorithms that can be used to expressing the augmented monomial symmetric functions in terms of the power sum symmetric functions. A simple way to express the augmented monomial symmetric function min terms of the power sum is given by Theorem 1 Let [ 1, 2, .
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