Related papers: A convolution for the complete and elementary symm…
We establish new properties of inhomogeneous spin $q$-Whittaker polynomials, which are symmetric polynomials generalizing $t=0$ Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come…
This work highlights the existence of partial symmetries in large families of iterated plethystic coefficients. The plethystic coefficients involved come from the expansion in the Schur basis of iterated plethysms of Schur functions indexed…
We give a new characterization of the vertical-strip LLT polynomials $\mathrm{LLT}_P(x;q)$ as the unique family of symmetric functions that satisfy certain combinatorial relations. This characterization is then used to prove an explicit…
We point out a simple criterion for convergence of polynomials to a concrete entire function in the Laguerre-P\'{o}lya ($\mathcal{LP}$) class (of all functions arising as uniform limits of polynomials with only real roots). We then use this…
Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we introduce and describe the…
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…
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of…
In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…
We consider two important families of BC_n-symmetric polynomials, namely Okounkov's interpolation polynomials and Koornwinder's orthogonal polynomials. We give a family of difference equations satisfied by the former, as well as…
We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
By applying p-adic integral on the set of p-adic integers in [27] (Interpolation Functions for New Classes Special Numbers and Polynomials via Applications of p-adic Integrals and Derivative Operator, Montes Taurus J. Pure Appl. Math. 3…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
We introduce a new family of symmetric polynomials $\mathfrak{G}^{(\mathbf{u},\mathbf{v})}_{\lambda}$ arising from exactly solvable lattice models associated with the quantised loop algebra $\mathcal{U}_{q}(\mathfrak{sl}_{2}[z^\pm])$. The…
A symmetry of $(t,q)$-Eulerian numbers of type $B$ is combinatorially proved by defining an involution preserving many important statistics on the set of permutation tableaux of type $B$. This involution also proves a symmetry of the…
We obtain some criteria for a symmetric square-central element of a totally decomposable algebra with orthogonal involution in characteristic two, to be contained in an invariant quaternion subalgebra.
We study the behavior of the initial coefficients of univalent functions under the Steiner symmetrization, and give some applications to functions of class \Sigma.
We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we…
The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate Stirling numbers of both kinds associated with degenerate hyperharmonic numbers and also with degenerate Bernolli, degenerate…
We present an elementary identity for the cyclotomic polynomials $\Phi_n(X)$ which reflects a kind of multiplicative property of $\Phi_n(X)$ as a function of $n$, and we explore its connections with the properties of other arithmetical…