tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Our aim in this paper is to discover special symmetric properties for twisted q-Genocchi polynomials. We are going to find a symmetric identity for twisted q-Genocchi zeta function. From property of the twis...

Standard algorithms for dealing with symmetric polynomials are presented using rewriting techniques. This is for instance the case of the ”fundamental theorem of symmetric polynomials”, which states that any symmetric polynomial is a polynomial in the elementary symmetric ones, and whose proof involves rewriting using a suitable elimination order. This kind approach usually spoils useful featur...

For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a symmetric scheme and a non-symmetric scheme. The general approach is illustrated by the examples of the classical orthogonal polynomials: Hermite, Jacobi and La...

Under mild conditions on n, p, we give a lower bound on the number of n-variable balanced symmetric polynomials over finite fields GF (p), where p is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we prove that X(2, 2`− 1) are balanced and conjecture that these are the only balanced symmetric polynomials over GF (2...

In (1.2) mκ(z) is the monomial symmetric function in the variables z1, . . . , zN , and the sum is over all partitions μ which have the same modulus as κ but are smaller in dominance ordering. The polynomials Pκ possess a host of special properties, and in fact form the natural basis for a class of symmetric multivariable orthogonal polynomials generalizing the classical orthogonal polynomials ...

In this note, a deep connection between free field realisations of conformal field theories and symmetric polynomials is presented. We give a brief introduction into the necessary prerequisites of both free field realisations and symmetric polynomials, in particular Jack symmetric polynomials. Then we combine these two fields to classify the irreducible representations of the minimal model vert...

The branching coefficients in the expansion of the elementary symmetric function multiplied by a symmetric Macdonald polynomial Pκ(z) are known explicitly. These formulas generalise the known r = 1 case of the Pieri-type formulas for the nonsymmetric Macdonald polynomials Eη(z). In this paper, we extend beyond the case r = 1 for the nonsymmetric Macdonald polynomials, giving the full generalisa...

Abstract. In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, such as the elementary, homogeneous, and power sum symmetric polynomials. We investigate properties of these families and focus on constructing their rational roots under a product induce...

in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...