相关论文: Unusual formulae for the Euler characteristic

We prove an algebraic formula for the Euler characteristic of the Milnor fibres of functions with critical locus a smooth curve on a space which is a weighted homogeneous complete intersection with isolated singularity.

In this paper, we define a parametric variant of generalized Euler sums and call them the (alternating) parametric Euler $T$-sums. By using the contour integration method and residue theorem, we establish several explicit formulae for the…

We compute the (primary) equivariant Euler characteristics of the building for the general linear group over a finite field.

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…

This paper defines the Euler-Poincar\'{e} characteristic of joint reductions of ideals which concerns the maximal terms in the Hilbert polynomial; characterizes the positivity of mixed multiplicities in terms of minimal joint reductions;…

We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…

We study several variants of Euler sums by using the methods of contour integration and residue theorem. These variants exhibit nice properties such as closed forms, reduction, etc., like classical Euler sums. In addition, we also define a…

We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples. In…

The Euler characteristic of the link of a real algebraic variety is an interesting topological invariant in order to discuss local topological properties. We prove in the paper that an invariant stronger than the Euler Characteristic is…

We represent excursion sets of smooth random fields as unions of a topological basis consisting of a sequence of simply and multiply connected compact subsets of the underlying manifold. The associated coefficients, which are non-negative…

This paper defines mixed multiplicity systems; the Euler-Poincare characteristic and the mixed multiplicity symbol of $\mathbb{N}^d$-graded modules with respect to a mixed multiplicity system, and proves that the Euler-Poincare…

We derive eight identities of symmetry in three variables related to generalized twisted Euler polynomials and alternating generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since…

This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…

Given a multiarrangement of hyperplanes we define a series by sums of the Hilbert series of the derivation modules of the multiarrangement. This series turns out to be a polynomial. Using this polynomial we define the characteristic…

We make calculations in graph homology which further understanding of the topology of spaces of string links, in particular calculating the Euler characteristics of finite-dimensional summands in their homology and homotopy. In doing so, we…

In this article, we focus on the characteristic polynomial of a graph containingloops, but without multiple edges. We present a relationship between thecharacteristic polynomial of a graph with loops and the graph obtained byremoving all…

The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we…

We exhibit a change of variables that maintains the Mahler measure of a given polynomial. This method leads to the construction of highly non-trivial polynomials with given Mahler measure and settles some conjectural numerical formulas due…

In this paper, we derive eight basic identities of symmetry in three variables related to $q$-Euler polynomials and the $q$-analogue of alternating power sums. These and most of their corollaries are new, since there have been results only…

The union of a collection of $n$ sets is generally expressed in terms of a characteristic (indicator) function that contains $2^{n}-1$ terms. In this article, a much simpler expression is found that requires the evaluation of $n$ terms…