Related papers: Minimal plus-one generated line arrangements with …

We deform monomial space curves in order to construct examples of set-theoretical complete intersection space curve singularities. As a by-product we describe an inverse to Herzog's construction of minimal generators of non-complete…

A discriminantal hyperplane arrangement B(n,k,A) is constructed from a given (generic) hyperplane arrangement A, which is classified as either very generic or non-very generic depending on the combinatorial structure of B(n,k,A). In…

We investigate closure operators and describe their properties for $E$-combinations and $P$-combinations of structures and their theories. We prove, for $E$-combinations, that the existence of a minimal generating set of theories is…

We present the universal theory of weak crossed biproducts, and we prove that every weak projection of weak bialgebras induces an example of this crossed structure. As an example, we give the construction of a weak projection of a weak…

Several authors have recently attempted to show that the intersection of three simply connected subcontinua of the plane is simply connected provided it is non-empty and the intersection of each two of the continua is path connected. In…

The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches,…

We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct sum of free groups, then the complements of the arrangements are homotopy equivalent. For…

*This paper is from 2018* In this paper, we try to classify moduli spaces of arrangements of $12$ lines with sextic points. We show that moduli spaces of arrangements of $12$ lines with sextic points can consist of more than two connected…

We provide a mini-guide to some of the possible manifestations of weak scale supersymmetry. For each of six scenarios we provide a brief description of the theoretical underpinnings, the adjustable parameters, a qualitative description of…

Sixteen new linear codes are presented: three of them improve the lower bounds on the minimum distance for a linear code and the rest are an explicit construction of unknown codes attaining the lower bounds on the minimum distance. They are…

We give an extended review of recent work on the extended weak coupling limit. Background material on completely positive semigroups and their unitary dilations is given, as well as a particularly easy construction of `quadratic noises'.

For an arrangement of $n$ pseudolines in the real projective plane let us denote by $t_i$ the number of vertices incident to $i$ lines. We obtain a linear on $t_i$ inequality similar to the Hirzebruch one, but with an elementary proof. We…

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoi\v{c}i\'{c} (2003) showed that the limiting set is dense…

We prove that all $1$-vertex spatial graphs with adequate diagrams have minimal crossing number, and that spatial graph diagrams obtained by replacing vertices and edges of a planar embedded graph by minimal crossing link or spatial graph…

A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…

We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some…

Using the concept of Geometric Weakly Admissible Meshes together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate least squares approximation and Lagrange…

The action of the mapping class group of the thrice-punctured projective plane on its $\mathrm{GL}(2,\mathbb{C})$ character variety produces an algorithm for generating the simple length spectra of quasi-Fuchsian thrice-punctured projective…

We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and…

We construct new examples of free curve arrangements in the complex projective plane using point-line operators recently defined by the second author. In particular, we construct a new example of a conic-line arrangement with ordinary…