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1.
In this paper, we deal with some corresponding relations between knots and polynomials by using the basic properties of knot polynomials (such as, some special values of knot polynomials, the Arf invariant and derivative of knot polynomials). We give necessary and sufficient conditions that a Laurent polynomial with integer coefficients, whose breadth is less than five, is the Jones polynomial of a certain knot.  相似文献   

2.
The purpose of this paper is to establish some identities with products of q- Hermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.  相似文献   

3.
In this paper we will study Dickson polynomials of the first and second kinds over finite fields. For these polynomials we will discuss some known properties, point out some similarities and differences between the two kinds, and most importantly, indicate a number of open problems concerning these polynomials.  相似文献   

4.
Some Identities Involving Square of Fibonacci Numbers and Lucas Numbers   总被引:8,自引:0,他引:8  
By studying the properties of Chebyshev polynomials, some specific and meaningful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbers and Lucas numbers are obtained.  相似文献   

5.
《分析论及其应用》2017,33(4):316-322
In this paper,we have studied the Lacunary type of polynomials and proved a result which generalizes as well as refines some well-known polynomial inequalities regarding the growth of polynomials not vanishing inside a circle.Further the paper corrects the proofs of some already known results.  相似文献   

6.
By means of generating function and partial derivative methods, we investigate and establish several general summation formulas involving two classes of polynomials. The general results would apply to yield some identities for the Pell polynomials and Pell-Lucas polynomials, and other general polynomials can also be recovered in this paper.  相似文献   

7.
In this paper, we define the self-inverse sequences related to sequences of polynomials of binomial type, and give some interesting results of these sequences. Moreover, we study the self-inverse sequences related to the Laguerre polynomials.  相似文献   

8.
In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous results, to degenerate Bernoulli polynomials and Korobov polynomials of the first kind and get some new identities. In addition, letting λ→ 0 in such identities gives us those for Bernoulli polynomials and Bernoulli polynomials of the second kind.  相似文献   

9.
In this paper, we deal with basic properties of some pretzel links and properties of the Jones polynomials of some pretzel links. By using these properties, the zero distribution of pretzel links is st...  相似文献   

10.
It is well known that Hall polynomials as structural coefficients play an important role in the structure of Lie algebras and quantum groups. By using the properties of representation categories of affine quivers, the task of computing Hall polynomials for affine quivers can be reduced to counting the numbers of solutions of some matrix equations. This method has been applied to obtain Hall polynomials for indecomposable representations of quivers of type Am(m≥1)  相似文献   

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