Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Schützenberger into standard bases. We prove that the resulting polynomials, which we call Demazure atoms, can be obtained from a certain specialization of nonsymmetric Macdonald polynomials. This combinatorial interpretation for Demazure atoms accelerates the computation of the right key...

Fibonacci polynomial sequence is an extension of sequence. Here we define a generalizing the integer which enumerates number subsets set [n] including no two consecutive even integers. The associated with polynomials. Some basic properties are obtained.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Abstract Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A ′ n +1 ( x ) = + 1) with 0 constant polynomial. This allows us to obtain in simple way some known relations involving Apostol-Bernoulli polynomials, Apostol-Euler and generalized Bernoulli attached primitive Dirichlet character.

Our objective in this paper is to present the sequence of Stancu type operators including generalized Brenke polynomials. We answer problem uniform approximation continuous functions on closed bounded interval and order convergence estimate by known tools theory. Furthermore, we apply some results obtained work Miller-Lee polynomials Gould-Hopper

In this article, a study is carried out around the Perrin sequence, these numbers marked by their applicability and similarity with Padovan’s numbers. With that, we will present recurrence for Perrin’s polynomials also definition of complex bivariate polynomials. From this, numbers, generating function, matrix Binet formula are defined.