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We show that the spaces $\mathcal{E}_{\{\omega\}}(\Omega)$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where $\omega$ is a quasianalytic weight function and $\Omega$ is an…
In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers
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…
Recently, the higher-order q-Euler polynomials and multiple q-Euler zeta functions are introduced by T. Kim ([8, 9]). In this paper, we investigate some symmetric properties of the multiple q-Euler zeta function and derive various…
We introduce inversions tableaux, a new combinatorial model for Schubert polynomials and Stanley symmetric functions that directly specializes to semi-standard Young tableaux in the Grassmannian case. They are a modification of the balanced…
In this paper, we use two different approaches to introduce $q$-analogs of Riemann's zeta function and prove that their values at even integers are related to the $q$-Bernoulli and $q$ Euler's numbers introduced by Ismail and Mansour…
We study the connection between stringy Betti numbers of Gorenstein toric varieties and the generating functions of the Ehrhart polynomials of certain polyhedral regions. We use this point of view to give counterexamples to Hibi's…
Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of ($q=1$) classical orthogonal polynomials, and study those cases in which the…
We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…
We study multiple orthogonal polynomials of type I and type II which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the…
We introduce a modular (integral) complementary polynomial $\kappa(G;x,y)$ ($\kappa_{\mathbbm z}(G;x,y)$) of two variables of a graph $G$ by counting the number of modular (integral) complementary tension-flows (CTF) of $G$ with an…
We prove a Chevalley formula for the equivariant quantum multiplication of two Schubert classes in the homogeneous variety X=G/P. As in the case when X is a Grassmannian, studied by the author in a previous paper, this formula implies an…
In this paper we give some interesting identities between Euler numbers and zeta functions. Finally we will give the new values of Euler zeta function at positive even integers.
The algebra B of bicomplex numbers is viewed as a complexification of the Archimedean f-algebra of hyperbolic numbers D. This lattice-theoretic approach allows us to establish new properties of the so-called D-norms. In particular, we show…
In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend…
In this paper two important classes of orthogonal polynomials in higher dimensions using the framework of Clifford analysis are considered, namely the Clifford-Hermite and the Clifford-Gegenbauer polynomials. For both classes an explicit…
Symmetric Grothendieck polynomials are analogues of Schur polynomials in the K-theory of Grassmannians. We build dual families of symmetric Grothendieck polynomials using Schur operators. With this approach we prove skew Cauchy identity and…
In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper,…
The derivative polynomials introduced by Knuth and Buckholtz in their calculations of the tangent and secant numbers are extended to a multivariable $q$--environment. The $n$-th $q$-derivatives of the classical $q$-tangent and $q$-secant…
The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1,x2,...]. We suggest the "prism tableau model" for these polynomials. A novel aspect of this alternative to earlier results is that it directly…