Related papers: Binomial Andrews-Gordon-Bressoud identities
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…
In this paper we prove some combinatorial identities which can be considered as generalizations and variations of remarkable Chu-Vandermonde identity. These identities are proved by using an elementary combinatorial-probabilistic approach…
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
Some ramifications of the identity of Chaundy and Bullard are presented. We discuss its homogeneous form and its relations to other identities, as well as extensions to more variables and more parameters.
Motivated by some binomial coefficients identities encountered in our approach to the enumeration of convex polyominoes, we prove some more general identities of the same type, one of which turns out to be related to a strange evaluation of…
In this paper we obtain several new identities for Bernoulli and Euler polynomials; some of them extend Miki's and Matiyasevich's identities. Our new method involves differences and derivatives of polynomials.
We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify Macdonald's normalization conjectures for these…
A generalization of the Chu-Vandermonde convolution is presented and proved with the integral representation method. This identity can be transformed into another identity, which has as special cases two known identities. Another identity…
We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.
In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
In this paper, we gave some properties of binomial coefficient.
Recently, Andrews and EI Bachraoui obtained several iden tities on two-colored partitions. While solving open problems they posed, Chen and Zhou derived a number of identities using analytic methods and asked for combinatorial proofs. In…
We prove certain Nahm-type sum representations for the (odd modulus) Andrews-Gordon identities, the (even modulus) Andrews-Bressoud identities, and Rogers' false theta functions. These identities are motivated on one hand by a recent work…
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
We prove a binomial formula for Macdonald polynomials and consider applications of it.
We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order…
We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.
The Rogers-Ramanujan identities and various analogous identities (Gordon, Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities concerned with integer partitions. These identities (written in generating function form)…