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1.
Engin Özkan  İpek Altun 《代数通讯》2013,41(10):4020-4030
In this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are generalized in the paper. Furthermore, we give relationships between the Fibonacci polynomials and the Lucas polynomials.  相似文献   

2.
Eisenstein polynomials, which were defined by Oura, are analogues of the concept of an Eisenstein series. Oura conjectured that there exist some analogous properties between Eisenstein series and Eisenstein polynomials. In this paper, we provide new analogous properties of Eisenstein polynomials and zeta polynomials. These properties are finite analogies of certain properties of Eisenstein series.  相似文献   

3.
主要研究勒让德多项式与契贝谢夫多项式之间的关系的性质,利用生成函数和函数级数展开的方法,得出了勒让德多项式与契贝谢夫多项式之间的一个重要关系,这对勒让德多项式与契贝谢夫多项式的研究有一定的推动作用.  相似文献   

4.
We classify all self-reciprocal polynomials arising from reversed Dickson polynomials over \(\mathbb {Z}\) and \(\mathbb {F}_p\), where p is prime. As a consequence, we also obtain coterm polynomials arising from reversed Dickson polynomials.  相似文献   

5.
The eigenvalues of the classical association schemes are given by certain Askey-Wilson polynomials (or limiting cases). Kernel polynomials of the Askey-Wilson polynomials are also Askey-Wilson polynomials. We determine when both the Askey-Wilson polynomials and their kernels are the eigenvalues for known association schemes.  相似文献   

6.
《Discrete Mathematics》2022,345(3):112714
We first present grammatical interpretations for the alternating Eulerian polynomials of types A and B. As applications, we then derive several properties of the type B alternating Eulerian polynomials, including recurrence relations, generating function and unimodality. And then, we establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials, which implies that the type B alternating Eulerian polynomials have gamma-vectors that alternate in sign.  相似文献   

7.
We give a direct proof of the combinatorial formula for interpolation Macdonald polynomials by introducing certain polynomials, which we call generic Macdonald polynomials, and which depend on d additional parameters and specialize to all Macdonald polynomials of degree d. The form of these generic polynomials is that of a Bethe eigenfunction and they imitate, on a more elementary level, the R-matrix construction of quantum immanants.  相似文献   

8.
The Adomian decomposition method is widely used in approximate calculation. The main difficulty of the method is to calculate Adomian polynomials, the procedure is very complex. In order to overcome the demerit, this paper suggests an alternative approach to Adomian method, instead of Adomian polynomials, He polynomials are introduced based on homotopy perturbation method. The solution procedure becomes easier, simpler, and more straightforward.  相似文献   

9.
A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements. This is a natural generalization of the familiar permutation polynomials. Basic properties of quasi-permutation polynomials are derived. General criteria for a quasi-permutation polynomial extending the well-known Hermite’s criterion for permutation polynomials as well as a number of other criteria depending on the permuted domain and range are established. Different types of quasi-permutation polynomials and the problem of counting quasi-permutation polynomials of fixed degree are investigated.  相似文献   

10.
The purpose of this paper is to define a new class polynomials. Special cases of these polynomials give many famous family of the Bernstein type polynomials and beta polynomials. We also construct generating functions for these polynomials. We investigate some fundamental properties of these functions and polynomials. Using functional equations and generating functions, we derive various identities related to theses polynomials. We also construct interpolation function that interpolates these polynomials at negative integers. Finally, we give a matrix representations of these polynomials. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

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