相关论文: On a Dehn-Sommerville functional for simplicial co…

This is a note on three graph parameters motivated by the Euler-Poincare characteristic for simplicial complex. We show those three graph parameters of a given connected graph $G$ is greater than or equal to that of the complete graph with…

We prove a Lefschetz formula for general simple graphs which equates the Lefschetz number L(T) of an endomorphism T with the sum of the degrees i(x) of simplices in G which are fixed by T. The degree i(x) of x with respect to T is defined…

We report on some properties of the $\xi(s)$ function and its value on the critical line, $\Xi(t)=\xi\left(\tfrac{1}{2}+it\right)$. First, we present some identities that hold for the log derivatives of a holomorphic function. We then…

We extend the circle of ideas from a previous paper on hypersurfaces to functions $f \colon (\mathbb C^n, 0) \to (\mathbb C^k, 0)$ with an isolated singularity in a stratified sense on an arbitrary, but fixed complex analytic germ $(X, 0)$.…

We introduce a family of regularized functionals $g_n(x)$ that generalize the Euler--Mascheroni constant $\gamma$. They arise from a weighted regularization of Clausen-type trigonometric sums, and admit explicit integral representations,…

The two-dimensional inhomogeneous zeta-function series (with homogeneous part of the most general Epstein type): \[ \sum_{m,n \in \mbox{\bf Z}} (am^2+bmn+cn^2+q)^{-s}, \] is analytically continued in the variable $s$ by using zeta-function…

We obtain first order linear partial differential equations which are satisfied by exponential generating functions of two variables for the number of connected bipartite graphs with given Betti number. By solving these equations…

We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for…

We generalize a formula due to Macdonald that relates the singular Betti numbers of $X^{n}/G$ to those of $X$, where $X$ is a compact manifold and $G$ is any subgroup of the symmetric group $S_{n}$ acting on $X^{n}$ by permuting…

Let F be a nonarchimedean locally compact field with residue characteristic p and G(F) the group of F-rational points of a connected reductive group. Following Schneider and Stuhler, one can realize, in a functorial way, any smooth complex…

We define discrete generating series for arbitrary functions \( f \colon \mathbb{Z}^n \rightarrow \mathbb{C} \) and derive functional relations that these series satisfy. For linear difference equations with constant coefficients, we…

A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…

We define zeta functions for the adjoint action of GL(n) on its Lie algebra and study their analytic properties. For n<4 we are able to fully analyse these functions, and recover the Shintani zeta function for the prehomogeneous vector…

The core of this article is a general theorem with a large number of specializations. Given a manifold $N$ and a finite number of one-parameter groups of point transformations on $N$ with generators $Y, X_{(1)}, \cdots, X_{(d)} $, we…

Given a square matrix with elements in the group-ring of a group, one can consider the sequence formed by the trace (in the sense of the group-ring) of its powers. We prove that the corresponding generating series is an algebraic…

We continue the study of the $k$-cut complex $\Delta_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jeli\'c Milutinovi\'c, Rowlands, Sundaram and Xue [Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2):…

For a simplicial complex K on m vertices and simplicial complexes K1,...,Km a composed simplicial complex K(K1,...,Km) is introduced. This construction generalizes an iterated simplicial wedge construction studied by A. Bahri, M. Bendersky,…

Given an infinite field $\mathbb{k}$ and a simplicial complex $\Delta$, a common theme in studying the $f$- and $h$-vectors of $\Delta$ has been the consideration of the Hilbert series of the Stanley--Reisner ring $\mathbb{k}[\Delta]$…

In this paper we study various simplicial complexes associated to the commutative structure of a finite group G. We define NC(G) (resp. C(G)) as the complex associated to the poset of pairwise non-commuting (resp. commuting) sets in G. We…

We define a D_0 graph to be a graph whose vertex set is a subset of permutations of n, with edges of the form ...bac... <--> ...bca... or ...acb... <--> ...cab... (Knuth transformations), or ...bac... <--> ...acb... or ...bca... <-->…