相关论文: Derivations and identities for Fibonacci and Lucas…

We study a recursively defined two-parameter family of graphs which generalize Fibonacci cubes and Pell graphs and determine their basic structural and enumerative properties. In particular, we show that all of them are induced subgraphs of…

We introduce the central Fubini-like numbers and polynomials using Rota approach. Several identities and properties are established as generating functions, recurrences, explicit formulas, parity, asymptotics and determinantal…

We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…

In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.

For every variety of algebras over a field, there is a natural definition of a corresponding variety of dialgebras (Loday-type algebras). In particular, Lie dialgebras are equivalent to Leibniz algebras. We use an approach based on the…

In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree.…

In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.

We consider an identity relating Fibonacci numbers to Pascal's triangle discovered by G. E. Andrews. Several authors provided proofs of this identity, most of them rather involved or else relying on sophisticated number theoretical…

In this paper, we give some determinantal and permanental representations of generalized bivariate Fibonacci p-polynomials by using various Hessenberg matrices. The results that we obtained are important since generalized bivariate…

Divisibility sequences are defined by the property that their elements divide each other whenever their indices do. The divisibility sequences that also satisfy a linear recurrence, like the Fibonacci numbers, are generated by polynomials…

In this paper, we construct Pell matrices, analogous to Fibonacci matrices, to study algebraic properties of Pell numbers via linear algebra. This framework yields identities involving the trace, inverse, and determinant, as well as matrix…

Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…

In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.

We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of…

We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.

In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have…

In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.

In this paper, we give some determinantal and permanental representations of Generalized Fibonacci Polynomials by using various Hessenberg matrices. These results are general form of determinantal and permanental representations of k…

A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If the pair of matrices are the same, they define a dual relationship. Here presented is a unified approach to construct dual relationships via…

Presented are polynomial identities which imply generalizations of Euler and Rogers--Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by…