First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also determine minimal structured perturbations for which approximate eigenelements are exact eigenelements of the perturbed polynomials. Next, we analyze the effe...

We consider two important families of BCn-symmetric polynomials, namely Okounkov’s interpolation polynomials and Koornwinder’s orthogonal polynomials. We give a family of difference equations satisfied by the former, as well as generalizations of the branching rule and Pieri identity, leading to a number of multivariate q-analogues of classical hypergeometric transformations. For the latter, we...

Abstract. Through an algebraic method using the Dunkl–Cherednik operators, the multivariable Hermite and Laguerre polynomials associated with the AN−1and BN Calogero models with bosonic, fermionic and distinguishable particles are investigated. The Rodrigues formulas of column type that algebraically generate the monic nonsymmetric multivariable Hermite and Laguerre polynomials corresponding to...

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called p, q -Fibonacci polynomials. We obtain combinatorial identities and by using Riordanmethodwe get factorizations of Pascal matrix involvin...

We prove generalized arithmetic-geometric mean inequalities for quasi-means arising from symmetric polynomials. The inequalities are satisfied by all positive, homogeneous symmetric polynomials, as well as a certain family of nonhomogeneous polynomials; this family allows us to prove the following combinatorial result for marked square grids. Suppose that the cells of a n × n checkerboard are e...

We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchange terms. For the non-symmetric Jack polynomials, the constant term normalization N is evaluated using recurrence relations, and N is related to the norm for the non-symmetric analogue of the power-sum i...

We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchange terms. For the non-symmetric Jack polynomials, the constant term normalization N η is evaluated using recurrence relations, and N η is related to the norm for the non-symmetric analogue of the power-s...

Symmetric polynomials and symmetric functions are ubiquitous in mathematics and mathematical physics. For example, they appear in elementary algebra (e.g. Viete’s Theorem), representation theories of symmetric groups and general linear groups over C or finite fields. They are also important objects to study in algebraic combinatorics. Via their close relations with representation theory, the th...