Related papers: Orientation of good covers

Given a finite set of points $C \subseteq \mathbb{R}^d$, we say that an ordering of $C$ is protrusive if every point lies outside the convex hull of the points preceding it. We give an example of a set $C$ of $5$ points in the Euclidean…

An oriented graph is a directed graph which can be obtained from a simple undirected graph by orienting its edges. In this paper we show that any oriented graph G on n vertices with minimum indegree and outdegree at least (1/2-o(1))n…

Let $k$ be a number field and $B$ be a central simple algebra over $k$ of dimension $p^2$ where $p$ is prime. In the case that $p=2$ we assume that $B$ is not totally definite. In this paper we study sets of pairwise nonisomorphic maximal…

Consider two horizontal lines in the plane. A pair of a point on the top line and an interval on the bottom line defines a triangle between two lines. The intersection graph of such triangles is called a simple-triangle graph. This paper…

An ordinary plane of a finite set of points in real 3-space with no three collinear is a plane intersecting the set in exactly three points. We prove a structure theorem for sets of points spanning few ordinary planes. Our proof relies on…

Metric embeddings traditionally study how to map $n$ items to a target metric space such that distance lengths are not heavily distorted; but what if we only care to preserve the relative order of the distances (and not their length)? In…

Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…

Consider three closed linear subspaces $C_1, C_2,$ and $C_3$ of a Hilbert space $H$ and the orthogonal projections $P_1, P_2$ and $P_3$ onto them. Halperin showed that a point in $C_1\cap C_2 \cap C_3$ can be found by iteratively projecting…

We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…

This exploratory paper considers the notion of a covering of a configuration and $G$-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot $G$-cover other…

We give a complete proof of Thurston's Orbifold Theorem for very good 3-orbifolds of cyclic type. An orbifold is said to be very good when it has a finite cover which is a manifold. A 3-orbifold is of cyclic type if the singular set is a…

We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…

We study the problem of finding an acyclic orientation of an undirected graph with constrained in-degree parities specified by a subset T of vertices. An orientation is called T -odd if a vertex v has odd in-degree if and only if v P T .…

A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not completely determine the triangulation. We show that even if…

Motivated by the recent result that left-orderability of a group $G$ is intimately connected to circular orderability of direct products $G \times \mathbb{Z}/n\mathbb{Z}$, we provide necessary and sufficient cohomological conditions that…

We show that the class of trapezoid orders in which no trapezoid strictly contains any other trapezoid strictly contains the class of trapezoid orders in which every trapezoid can be drawn with unit area. This is different from the case of…

A three-tope committee K* for a simple oriented matroid M is a 3-subset of its maximal covectors such that every positive halfspace of M contains at least two topes from K*. We consider three-tope committees as the vertex sets of triangles…

Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…

A \textit{$3$-net} of order $n$ is a finite incidence structure consisting of points and three pairwise disjoint classes of lines, each of size $n$, such that every point incident with two lines from distinct classes is incident with…

In this paper we show that a third order PDE system that is a general form of a CR-geometry PDE system has at most a ten-dimensional Lie symmetry algebra. We also show that this estimate is precise.