相关论文: Ehrhart polynomials and stringy Betti numbers

In this paper we study topology of the variety of closed planar polygons with given side lengths. We describe the Betti numbers of the moduli spaces as functions of the length vector. We also find sharp upper bounds on the sum of Betti…

We investigate the logarithmic bundles associated to arrangements of hypersurfaces with a fixed degree in a smooth projective variety. We then specialize to the case when the variety is a quadric hypersurface and a multiprojective space to…

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the…

Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…

The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…

A generic orthotope is an orthogonal polytope whose tangent cones are described by read-once Boolean functions. The purpose of this note is to develop a theory ofEhrhart polynomials for integral generic orthotopes. The most remarkable part…

We discuss inequalities between the values of \emph{homotopical and cohomological Poincar\'e polynomials} of the self-products of rationally elliptic spaces. For rationally elliptic quasi-projective varieties, we prove inequalities between…

Let S=K[X_1,...,X_n] be the polynomial ring over a field K. For bounded below Z^n-graded S-modules M and N we show that if Tor^S_p(M,N) is nonzero, then for every i between 0 and p, the dimension of the K-vector space Tor^S_i(M,N) is at…

In this paper, by using some families of special numbers and polynomials with their generating functions, we give various properties of these numbers and polynomials. These numbers are related to the well-known numbers and polynomials,…

In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.

The article is devoted to the problem of Hilbert-Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary matrix group endowed with an invariant probability measure. An orthogonal basis of Hilbert-Schmidt…

We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also…

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if…

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 a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-$D$ Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the…

In this paper, we find explicit formulas for higher order derivatives of the inverse tangent function. More precisely, we study polynomials which are induced from the higher-order derivatives of arctan(x). Successively, we give generating…

We prove that the Ehrhart polynomial of a zonotope is a specialization of the multiplicity Tutte polynomial. We derive some formulae for the volume and the number of integer points of the zonotope.

We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…

We use Young's raising operators to introduce and study double eta polynomials, which are an even orthogonal analogue of Wilson's double theta polynomials. Our double eta polynomials give Giambelli formulas which represent the equivariant…

We investigate the roots of Hilbert quasipolynomials arising from certain rational generating functions.