Related papers: On the Ext Analog of the Euler Characteristic

We study the asymptotical behaviour of the moduli space of morphisms of given anticanonical degree from a rational curve to a split toric variety, when the degree goes to infinity. We obtain in this case a geometric analogue of Manin's…

The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded…

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

We define the Euler number of a bipartite graph on $n$ vertices to be the number of labelings of the vertices with $1,2,...,n$ such that the vertices alternate in being local maxima and local minima. We reformulate the problem of computing…

We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain weights.From these, we obtain some…

We write the Euler characteristic X(G) of a four dimensional finite simple geometric graph G=(V,E) in terms of the Euler characteristic X(G(w)) of two-dimensional geometric subgraphs G(w). The Euler curvature K(x) of a four dimensional…

Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…

We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers,…

The Euler characteristic was defined for finite strict n-categories by Leinster using the theory of enriched categories. This was an extension of some of his earlier work, which defined Euler characteristic for finite categories. Building…

Let $c$ be a characteristic form of degree $k$ which is defined on a Kaehler manifold of real dimension $m>2k$. Taking the inner product with the Kaehler form $\Omega^k$ gives a scalar invariant which can be considered as a generalized…

The history of the elastica is examined through the works of various contributors, including those of Jacob and Daniel Bernoulli, since its first appearance in a 1690 contest on finding the profile of a hanging flexible cord. Emphasis will…

The classical Euler's problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories…

Let $E_p(x)$ denote the Artin-Hasse exponential and let $\overline{E}_p(x)$ denote its reduction modulo $p$ in $\mathbb{F}_p[[x]]$. In this article we study transcendence properties of $\overline{E}_p(x)$ over $\mathbb{F}_p[x]$. We give two…

We prove that a certain eventually homological isomorphism between module categories induces a triangle equivalence between their singularity categories, Gorenstein defect categories and the stable categories of Gorenstein projective…

Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…

For Weyl groups of classical types, we present formulas to calculate the restriction of Springer representations to a maximal parabolic subgroup of the same type. As a result, we give recursive formulas for Euler characteristics of Springer…

We consider the independence complexes of square grids with cylindrical boundary conditions. When one of the dimensions is small we use simple reductions induced by edge removals to show explicit natural homotopy equivalences between those…

The double zeta function is a function of two arguments defined by a double Dirichlet series, and was first studied by Euler in response to a letter from Goldbach in 1742. By calculating many examples, Euler inferred a closed form…

We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We show that if X is a smooth affine scheme of dimension d over a field k of finite 2-cohomological dimension (with char(k)…

We consider $L$-functions $L_1,\ldots,L_k$ from the Selberg class which have polynomial Euler product and satisfy Selberg's orthonormality condition. We show that on every vertical line $s=\sigma+it$ with $\sigma\in(1/2,1)$, these…