相关论文: Orbifold Euler Characteristics of $\overline{\math…
We consider integrals of type $\int_{O_n}u_{11}^{a_1}... u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such…
We present an operator approach to Rogers-type formulas and Mehler's formulas for the Al-Salam-Carlitz polynomials $U_n(x,y,a;q)$. By using the q-exponential operator, we obtain a Rogers-type formula which leads to a linearization formula.…
We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
Binomial-Eulerian polynomials were introduced by Postnikov, Reiner and Williams. In this paper, properties of the binomial-Eulerian polynomials, including recurrence relations and generating functions are studied. We present three…
We use the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized…
We are extending results from \cite{B-Hurwitz} by building a parallel theory of simple Hurwitz numbers for the reflection groups $G(m,1,n)$. We also study analogs of the cut-and-join operators. An algebraic description as well as a…
Orthogonal polynomials for a family of weight functions on $[-1,1]^2$, $$ \CW_{\a,\b,\g}(x,y) = |x+y|^{2\a+1} |x-y|^{2\b+1} (1-x^2)^\g(1-y^2)^{\g}, $$ are studied and shown to be related to the Koornwinder polynomials defined on the region…
We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of…
We compute the Euler characteristic with compact supports $\chi_c$ of the formal barycenter spaces with weights of a finite CW complex, connected or not. This reduces to the topological Euler characteristic $\chi$ when the weights of the…
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.
In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…
Given a countable residually finite group $\Gamma$, we write $\Gamma_n \to e$ if $(\Gamma_n)$ is a sequence of normal subgroups of finite index such that any infinite intersection of $\Gamma_n$'s contains only the unit element $e$ of…
We present an algorithm for the symbolic and numerical computation of the degrees of the Chern-Schwartz-MacPherson classes of a closed subvariety of projective space P^n. As the degree of the top Chern-Schwartz-MacPherson class is the…
The incompressible Euler equations on a compact Riemannian manifold $(M,g)$ take the form \begin{align*} \partial_t u + \nabla_u u &= - \mathrm{grad}_g p \mathrm{div}_g u &= 0. \end{align*} We show that any quadratic ODE $\partial_t y =…
In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have…
Studying the virtual Euler characteristic of the moduli space of curves, Harer and Zagier compute the generating function $C_g(z)$ of unicellular maps of genus $g$. They furthermore identify coefficients, $\kappa^{\star}_{g}(n)$, which…
The KP and 2D Toda tau-functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion programme. A graphical representation of such weighted…
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the…
The purpose of this note is to prove an Euler-type formula for partitions of the M\"obius strip. This formula was introduced in our joint paper with R.~Kiwan, "Courant-sharp property for Dirichlet eigenfunctions on the M\"obius strip"…