Related papers: A Generalization of Tepper's Identity

In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.

In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a…

We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…

In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.

Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…

A generalization of Newton's identity on symmetric functions is given. Using the generalized Newton identity we give a unified method to show the existence of Hall-Littlewood, Jack and Macdonald polynomials. We also give a simple proof of…

In this article, a short combinatorial proof of the Capelli's identity is given. It also leads to an easy proof of the Capelli--Cauchy--Binet identity, a more general form of Capelli's identity. With the technique introduced, the Turnbull's…

We present a generalization of the Newton-Girard identities, along with some applications. As an addendum, we collect many evaluations of symmetric polynomials to which these identities apply.

We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…

In this article we obtain a general polynomial identity in $k$ variables, where $k\geq 2$ is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a $k \times k$ matrix.…

The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.

Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely…

We provide the polynomial identities of algebras that are both generalized Poisson algebras and transposed Poisson algebras. We establish defining identities via single operation for generalized Poisson algebras and prove that Ito's theorem…

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…

We prove an identity about partitions with a very elementary formulation. We had previously conjectured this identity, encountered in the study of shifted Jack polynomials (math.CO/9901040). The proof given is using a trivariate generating…

Recently the second named author discovered a combinatorial identity in the context of vertex representations of quantum Kac-Moody algebras. We give a direct and elementary proof of this identity. Our method is to show a related identity of…

Sylvester's identity is a classical determinantal identity with a straightforward linear algebra proof. We present a new, combinatorial proof of the identity, prove several non-commutative versions, and find a $\beta$-extension that is both…

In this paper we prove the identity that generalizes the Andrews-Gordon identity. Also we discuss the relation of our formula to the geometry of affine flag varieties and to the geometry of polyhedra.

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 the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all $2$-dimensional algebras with respect to these identities is…