On the Schur-Szegö composition of polynomials
نویسندگان
چکیده
The Schur-Szegö composition of two polynomials of degree ≤ n introduces an interesting semigroup structure on polynomial spaces and is one of the basic tools in the analytic theory of polynomials, see [5]. In the present paper we show how it interacts with the stratification of polynomials according to the multiplicities of their zeros and we present the induced semigroup structure on the set of all ordered partitions of n. To cite this article: V. Kostov, B. Shapiro, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
منابع مشابه
On Schur-szegö Composition of Polynomials
Schur-Szegö composition of two polynomials of degree less or equal than a given positive integer n introduces an interesting semigroup structure on polynomial spaces and is one of the basic tools in the analytic theory of polynomials, see [4]. In the present paper we add several (apparently) new aspects to the previously known properties of this operation. Namely, we show how it interacts with ...
متن کاملRogers–szegö Polynomials and Hall–littlewood Symmetric Functions
Here λ denotes a partition, λ its conjugate, and the condition “λ even” (or “λ even”) implies that all parts of λ (or all parts of λ) must be even. Furthermore, sλ(x) = sλ(x1, x2, . . . ) is a Schur function of a finite or infinite number of variables. When x = (x1, . . . , xn) the identities (1.1a)–(1.1c) may be viewed as reciprocals of Weyl denominator formulas; the latter expressing the prod...
متن کاملNarayana numbers and Schur-Szego composition
In the present paper we find a new interpretation of Narayana polynomials Nn(x) which are the generating polynomials for the Narayana numbers Nn,k = 1 n C k−1 n C k n where C i j stands for the usual binomial coefficient, i.e. C j = j! i!(j−i)! . They count Dyck paths of length n and with exactly k peaks, see e.g. [13] and they appeared recently in a number of different combinatorial situations...
متن کاملApproximation with Bernstein-Szegö polynomials
We present approximation kernels for orthogonal expansions with respect to Bernstein-Szegö polynomials. The construction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein-Szegö polynomials.
متن کاملRow-strict quasisymmetric Schur functions
Haglund, Luoto, Mason, and van Willigenburg introduced a basis for quasisymmetric functions called the quasisymmetric Schur function basis, generated combinatorially through fillings of composition diagrams in much the same way as Schur functions are generated through reverse column-strict tableaux. We introduce a new basis for quasisymmetric functions called the row-strict quasisymmetric Schur...
متن کامل