Related papers: Binomial Andrews-Gordon-Bressoud identities
In this paper, we give some interesting and new identities of q-Bernoulli numbers which are derived from convolutions on the ring of p-adic integers.
We prove a curious identity for the Bernoulli numbers.
We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on…
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…
The G\"ollnitz-Gordon identities were found by G\"ollnitz and Gordon independently. In 1967, Andrews obtained a combinatorial generalization of the G\"ollnitz-Gordon identities, called the Andrews-G\"ollnitz-Gordon theorem. In 1980,…
I revisit Bressoud's generalised Borwein conjecture. Making use of certain positivity-preserving transformations for q-binomial coefficients, I establish the truth of infinitely many new cases of the Bressoud conjecture. In addition, I…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
We give a commutative algebra viewpoint on Andrews recursive formula for the partitions appearing in "Gordon's identities", which are a generalization of Rogers-Ramanujan identities. Using this approach and differential ideals we conjecture…
Identities between Whittaker and modified Bessel functions are derived for particular complex orders. Certain polynomials appear in such identities, which satisfy a fourth order differential equation (not of hypergeometric type), and they…
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic…
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters. Several corollaries and examples are presented which are…
Several models for the Burnside bicategory of groupoids are described and shown to be equivalent. As observed by the late Gaunce Lewis, the corresponding Burnside category is additive.
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 a recent paper, Griffin, Ono and Warnaar present a framework for Rogers-Ramanujan type identities using Hall-Littlewood polynomials to arrive at expressions of the form \[\sum_{\lambda : \lambda_1 \leq m}…
Given an arbitrary ordered pair of coprime integers (a,b) we obtain a pair of identities of the Rogers--Ramanujan type. These identities have the same product side as the (first) Andrews--Gordon identity for modulus 2ab\pm 1, but an…
We construct new invariants of equivariant birational isomorphisms taking values in equivariant Burnside groups.
The binomial multichannel algorithm is proposed. Some its properties are discussed.
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 give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.
We present what we call a "motivated proof" of the Bressoud-G\"ollnitz-Gordon partition identities. Similar "motivated proofs" have been given by Andrews and Baxter for the Rogers-Ramanujan identities and by Lepowsky and Zhu for Gordon's…