Related papers: Planar Linkages and Algebraic Sets

The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…

Geometrical constructions using flexible cords have been known since the earliest days of recorded mathematics. In this paper we introduce rigorous definitions for two classes of string networks. A taut network is one in which all cords are…

We construct a completed version C(Gamma) of the configuration space of a linkage Gamma in R^3 which takes into account the ways one link can touch another. We also describe a simplified version of C(Gamma) which is a blow-up of the space…

Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…

The main result of this article is the decomposition of tensor products of representations of SL(2) in the sum of irreducible representations parametrized by outerplanar graphs. An outerplanar graph is a graph with the vertices 0, 1, 2,…

An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…

In the paper, we study special configurations of lines and points in the complex projective plane, so called k-nets. We describe the role of these configurations in studies of cohomology on arrangement complements. Our most general result…

In this paper, we study fan-planar drawings that use $h$ layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter…

We proved in another paper that every connected graph can be realized as the cut locus of some point on some riemannian surface. Here we give upper bounds on the number of such realizations.

This paper studies the relation between node deletion and algebraic connectivity for graphs with a hierarchical structure represented by layers. To capture this structure, the concepts of layered path graph and its (sub)graph cone are…

We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…

A projective rectangle is like a projective plane that may have different lengths in two directions. We develop properties of the graph of lines, in which adjacency means having a common point, especially its strong regularity and clique…

For a planar graph with a given f-vector $(f_{0}, f_{1}, f_{2}),$ we introduce a cubic polynomial whose coefficients depend on the f-vector. The planar graph is said to be real if all the roots of the corresponding polynomial are real. Thus…

Let $G$ be a graph that is topologically embedded in the plane and let $\mathcal{A}$ be an arrangement of pseudolines intersecting the drawing of $G$. An aligned drawing of $G$ and $\mathcal{A}$ is a planar polyline drawing $\Gamma$ of $G$…

In a planar L-drawing of a directed graph (digraph) each edge e is represented as a polyline composed of a vertical segment starting at the tail of e and a horizontal segment ending at the head of e. Distinct edges may overlap, but not…

We characterize and classify completely the planar 4R closed chain working on the Minkowskian plane. Our work would open a new research direction in the theory of geometric designs: the classification and characterization of the geometric…

Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…

An orthogonality space is a set equipped with a symmetric, irreflexive relation called orthogonality. Every orthogonality space has an associated complete ortholattice, called the logic of the orthogonality space. To every poset, we…

A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…

A map between operator spaces is called completely coarse if the sequence of its amplifications is equi-coarse. We prove that all completely coarse maps must be $\mathbb R$-linear. On the opposite direction of this result, we introduce a…