Augmented monomials in terms of power sums
نویسنده
چکیده
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.
منابع مشابه
MONOMIALS AS SUMS OF k-POWERS OF FORMS
Motivated by recent results on the Waring problem for polynomial rings [FOS12] and representation of monomial as sum of powers of linear forms [CCG12], we consider the problem of presenting monomials of degree kd as sums of kth-powers of forms of degree d. We produce a general bound on the number of summands for any number of variables which we refine in the two variables case. We completely so...
متن کاملMonomials as Sums of Powers: the Real Binary Case
We generalize an example, due to Sylvester, and prove that any monomial of degree d in R[x0, x1], which is not a power of a variable, cannot be written as a linear combination of fewer than d powers of linear forms.
متن کاملFormal Power Series and Their Continued Fraction Expansion
We note that the continued fraction expansion of a lacunary formal power series is a folded continued fraction with monomial partial quotients, and with the property that its convergents have denominators that are the sums of distinct monomials, that is, they are polynomials with coefficients 0, 1, and −1 only. Our results generalise, simplify and refine remarks of a previous note ‘Convergents ...
متن کاملOn Fibonacci Polynomial Expressions for Sums of mth Powers, their implications for Faulhaber’s Formula and some Theorems of Fermat
Denote by Σnm the sum of the m-th powers of the first n positive integers 1m + 2m + . . .+ nm. Similarly let Σrnm be the r-fold sum of the m-th powers of the first n positive integers, defined such that Σn = nm, and then recursively by Σn = Σr1m+Σr2m+ . . .+Σrnm. During the early 17th-century, polynomial expressions for the sums Σrnm and their factorisation and polynomial basis representation p...
متن کاملBottom Schur Functions
We give a basis for the space spanned by the sum ŝλ of the lowest degree terms in the expansion of the Schur symmetric functions sλ in terms of the power sum symmetric functions pμ, where deg(pi) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned by ŝλ, where λ is a partition of n, is equal to the number of partitions of n into pa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره 4 شماره
صفحات -
تاریخ انتشار 2015