Fedor V Fomin,Petr A Golovach,Tanmay Inamdar et al.
Fedor V Fomin et al.
The problem of packing of equal disks (or circles) into a rectangle is a fundamental geometric problem. (By a packing here we mean an arrangement of disks in a rectangle without overlapping.) We consider the following algorithmic generaliza...
Krishnendu Bhowmick,Oliver Roche-Newton
Krishnendu Bhowmick
An arc in F q 2 is a set P ⊂ F q 2 such that no three points of P are collinear. We use the method of hypergraph containers to prove several counting results for arcs. Let A ( q ) denote the family of all arcs in F q 2 . Our main...
Benny Sudakov,István Tomon
Benny Sudakov
Given positive integers k ≤ d and a finite field F , a set S ⊂ F d is (k, c)-subspace evasive if every k-dimensional affine subspace contains at most c elements of S. By a simple averaging argument, the maximum size of a (k, ...
Unbounded Regions of High-Order Voronoi Diagrams of Lines and Line Segments in Higher Dimensions [0.03%]
高维直线和线段的高阶Voronoi图的无界区域
Gill Barequet,Evanthia Papadopoulou,Martin Suderland
Gill Barequet
We study the behavior at infinity of the farthest and the higher-order Voronoi diagram of n line segments or lines in a d-dimensional Euclidean space. The unbounded parts of these diagrams can be encoded by a Gaussian map on the sphere of d...
Nóra Frankl,Dora Woodruff
Nóra Frankl
A recent generalization of the Erdős Unit Distance Problem, proposed by Palsson, Senger, and Sheffer, asks for the maximum number of unit distance paths with a given number of vertices in the plane and in 3-space. Studying a variant of thi...
Felix Dellinger
Felix Dellinger
This paper studies the discrete differential geometry of the checkerboard pattern inscribed in a quadrilateral net by connecting edge midpoints. It turns out to be a versatile tool which allows us to consistently define principal nets, Koen...
Terence Tao
Terence Tao
A well-known open problem of Meir and Moser asks if the squares of sidelength 1/n for n≥2 can be packed perfectly into a rectangle of area ∑n=2∞n-2=π2/6-1. In this paper we show that for any 1/2
Oscar Ortega-Moreno
Oscar Ortega-Moreno
Ball's complex plank theorem states that if v1,⋯,vn are unit vectors in Cd, and t1,⋯,tn are non-negative numbers satisfying ∑k=1ntk2=1, then there exists a unit vector v in Cd for which |⟨vk,v⟩|≥tk for ...
Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs [0.03%]
在完全图的简单绘制中以曲折方式寻找平面结构
Oswin Aichholzer,Alfredo García,Javier Tejel et al.
Oswin Aichholzer et al.
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). A simple drawing is c-monotone if there is a point O such that each ray emana...
Alexander Baumann,Haim Kaplan,Katharina Klost et al.
Alexander Baumann et al.
Let S⊆R2 be a set of n sites in the plane, so that every site s∈S has an associated radius rs>0. Let D(S) be the disk intersection graph defined by S, i.e., the graph with vertex set S and an edge between two distinct sites s,t&...