Related papers: Orientation of good covers
The set \[ \overline{\mathbb{E}}= \{ x \in {\mathbb{C}}^3: \quad 1-x_1 z - x_2 w + x_3 zw \neq 0 \mbox{ whenever } |z| < 1, |w| < 1 \} \] is called the tetrablock and has intriguing complex-geometric properties. It is polynomially convex,…
The 3D index of Dimofte-Gaiotto-Gukov a partially defined function on the set of ideal triangulations of 3-manifolds with $r$ torii boundary components. For a fixed $2r$ tuple of integers, the index takes values in the set of $q$-series…
We show that every bipartite planar graph with minimum degree at least 3 has proper orientation number at most 3.
A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were…
We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of…
We consider arbitrary orderings of the edges entering each vertex of the (downward directed) Pascal graph. Each ordering determines an adic (Bratteli-Vershik) system, with a transformation that is defined on most of the space of infinite…
We derive explicitly the structural properties of the $p$-adic special orthogonal groups in dimension three, for all primes $p$, and, along the way, the two-dimensional case. In particular, starting from the unique definite quadratic form…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
Starting from the classical notion of an oriented congruence (i.e. a foliation by oriented curves) in $R^3$, we abstract the notion of an oriented congruence structure. This is a 3-dimensional CR manifold $(M,H, J)$ with a preferred…
Given a right triangle ABC, with the ninety degree angle at A; consider the triangle O1OO2.Where the point O is the midpoint of the hypotenuseBC(and so the center of the triangle ABC's circumcircle), the point O1 being the triangle AOB's…
Results of Perron and Rolfsen imply that untwisted hyperbolic once-punctured torus bundles over the circle have bi-orderable fundamental groups. They do this by showing that the action of the monodromy preserves a "standard" bi-ordering…
We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus, we introduce and…
We classify the extensions of n-body central configurations to (n + 1)-body central configurations in R3, in both the collinear case and the non-collinear case. We completely solve the two open questions posed by Hampton (Nonlinearity 18:…
In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…
We formulate a model for magnetic and superconducting ordering at LaAlO3/SrTiO3 interfaces containing both localized magnetic moments and itinerant electrons. Though these both originate in Ti 3d orbitals, the former may be due to electrons…
We report on first principles Self-Interaction Corrected LSD (SIC-LSD) calculations of electronic structure of LaMnO$_{3}$ in the cubic phase. We found a strong tendency to localisation of the Mn $e_{g}$ electron and to orbital ordering. We…