Related papers: A q-Analog of Dual Sequences with Applications

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

We investigate some interesting properties of Bernstein polynomials associated with boson p-adic integrals on Zp.

We will prove an identity involving refined $q$-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined $q$-trinomials in an…

A characterization is given of those sequences of quasi-orthogonal polynomials which form also $q$-Appell sets.

We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.

In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfying moment conditions, we use the generating function of these…

In this note, we prove some combinatorial identities and obtain a simple form of the eigenvalues of $q$-Kneser graphs.

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

In this paper, we obtain a generalization of an identity due to Carlitz on Bernoulli polynomials. Then we use this generalized formula to derive two symmetric identities which reduce to some known identities on Bernoulli polynomials and…

The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…

In this paper, we investigate the properties of symmetry in two variables related to multiple Euler q-l-function which interpolates higher-order q-Euler polynomials at negative integers. From our investigation, we can derive many…

We present a few combinatorial identities which were encountered in our work on the spectral theory of quantum graphs. They establish a new connection between the theory of random matrix ensembles and combinatorics.

In 2009, Sagan and Savage introduced a combinatorial model for the Fibonomial numbers, integer numbers that are obtained from the binomial coefficients by replacing each term by its corresponding Fibonacci number. In this paper, we present…

In this paper we consider the extended q-Bernstein polynomials which are constructed by T. Kim and we investigate some properties.

We give combinatorial proofs of $q$-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the $q$-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel…

Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.

In the context of generating uniform random contingency tables with pre-specified marginals, the number of (binary) matrices with given row- and column-sums is a well-studied object in the literature. We will denote this number by $N(p,q)$,…

In this paper, we give some new identities of symmetry for q-Bernoulli polynomials under the symmetric group of degree n arising from p-adic q-integrals on Zp.

We prove polynomial boson-fermion identities for the generating function of the number of partitions of $n$ of the form $n=\sum_{j=1}^{L-1} j f_j$, with $f_1\leq i-1$, $f_{L-1} \leq i'-1$ and $f_j+f_{j+1}\leq k$. The bosonic side of the…

We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…