Related papers: Configuration Spaces of Points: A User's Guide
A circle graph is a graph in which the adjacency of vertices can be represented as the intersection of chords of a circle. The problem of calculating the chromatic number is known to be NP-complete, even on circle graphs. In this paper, we…
In this lecture series I will give a fundamental insight into configuration space techniques which are of help to calculate a broad class of Feynman diagrams, the sunrise-type diagrams. Applications are shown along with basic concepts and…
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very…
We extract an exact formula relating the number of lattice points in an expanding region of a complex semi-simple symmetric space and the automorphic spectrum from a spectral identity, which is obtained by producing two expressions for the…
This document is a companion for the Maple program \textbf{Summing a polynomial function over integral points of a polygon}. It contains two parts. First, we see what this programs does. In the second part, we briefly recall the…
We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincar\'{e} profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by…
Given a finite simple connected graph $\Gamma$, the graphical configuration space $\mathrm{Conf}_{\Gamma}(X)$ is the space of collections of points in $X$ indexed by the vertices of $\Gamma$, where points corresponding to adjacent vertices…
We define the independence ratio and the chromatic number for bounded, self-adjoint operators on an L^2-space by extending the definitions for the adjacency matrix of finite graphs. In analogy to the Hoffman bounds for finite graphs, we…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
Using the definition of colouring of $2$-edge-coloured graphs derived from $2$-edge-coloured graph homomorphism, we extend the definition of chromatic polynomial to $2$-edge-coloured graphs. We find closed forms for the first three…
I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…
By using Oprea's Bialynicki-Birula decomposition for the stack of genus zero stable maps to flag manifolds. We calculate the Poincar\'e polynomial of the moduli space in degree one and degree two.
We present coincidence and common fixed point results of selfmappings satisfying a contraction type in partially ordered metric spaces. As an application, we give an existence theorem for a common solution of integral equations.
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this…
Chromatic maps for spherical tensor categories are instrumental tools to construct (non semisimple) invariants of 3-manifolds and their extension to (non compact) (2+1)-TQFTs. In this paper, we introduce left and right chromatic maps for…
The orbital bivariate chromatic polynomial, introduced in this article, counts the number of ways to color the vertices of a graph with $\lambda$ colors such that adjacent vertices either receive distinct colors from a set of $\lambda$…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
This paper introduces the historical development of the symmetries for describing magnetic structures culminating in the derivation of the black and white and colored space groups. Beginning from the Langevin model of the Curie law, it aims…
The main result is a common generalization of results on lower bounds for the chromatic number of r-uniform hypergraphs and some of the major theorems in Tverberg-type theory, which is concerned with the intersection pattern of faces in a…