On Newton Interpolation of Symmetric Functions: A Characterization of Interpolation Macdonald Polynomials
نویسندگان
چکیده
منابع مشابه
Symmetric Functions and Macdonald Polynomials
The ring of symmetric functions Λ, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the symmetric group. One may define a coproduct on Λ by the plethystic addition on alphabets. In this way the ring of symmetric functions becomes a Hopf algebra. The Littlewood–...
متن کاملNONSYMMETRIC INTERPOLATION MACDONALD POLYNOMIALS AND gln BASIC HYPERGEOMETRIC SERIES
The Knop–Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gln. Our main results include a new q-binomial theorem, new q-Gauss sum, and several transformation formulae for gln series.
متن کاملOn Multiple Interpolation Functions of the q-Genocchi Polynomials
Recently, many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work New approach to q-Euler, Genocchi numbers and their interpolation functions, “Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105– 112, 2009.”, Kim defined new generating functions of q-Genocchi, q-Euler polynomials, and their interpolation functions. In ...
متن کاملQuantum interpolation of polynomials
Can a quantum computer efficiently interpolate polynomials? We consider blackbox algorithms that seek to learn information about a polynomial f from input/output pairs (xi, f(xi)). We define a more general class of (d, S)-independent function properties, where, outside of a set S of exceptions, knowing d input values does not help one predict the answer. There are essentially two strategies to ...
متن کاملOn interpolation by radial polynomials
A lemma of Micchelli’s, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback’s more recent extension of this lemma and Schaback’s result concerning interpolation by radial polynomials. Schaback’s interpolant is explored. In his most-cited paper, [M], Micchelli supplies the following interesting auxiliary lemma (h...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1998
ISSN: 0196-8858
DOI: 10.1006/aama.1998.0590