Augmented monomials in terms of power sums

Any positive integer n can be written as a sum of one or more positive integers, i.e., When the order of integers i does not matter, this representation is known as an integer partition Andrews (1976) and can be rewritten as where each positive integer i appears ti times. If the order of integers i is important, then the representation (1) is known as a composition. For we have a descending composition. We notice that more often than not there appears the tendency of defining partitions as descending compositions and this is also the con-vention used in this paper. In order to indicate that is a partition of n, we use the notation ⊢ n. We denote by l() the number of parts of , i.e., (1)n = 1 + 2 + · · · + r. n = t1 + 2t2 + · · · + ntn 1 2 · · · r = [1, 2,..., r] or = [1 t12t2... ntn] l() = r or l() = t1 + t2 + · · · + tn. 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 symmet-ric 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