Roman Prosanov
Roman Prosanov
We show that a convex body admits a translative dense packing in R d if and only if it admits a translative economical covering. ...
Stefan Felsner,Manfred Scheucher
Stefan Felsner
A pseudocircle is a simple closed curve on the sphere or in the plane. The study of arrangements of pseudocircles was initiated by Grünbaum, who defined them as collections of simple closed curves that pairwise intersect in exactly two cro...
Franz Aurenhammer,Gernot Walzl
Franz Aurenhammer
We give a concise definition of mitered offset surfaces for nonconvex polytopes in R 3 , along with a proof of existence and a discussion of basic properties. These results imply the existence of 3D straight skeletons for general nonconve...
Peter Franek,Marek Krčál
Peter Franek
The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f : K → R n on a compact space K that are invariant with respect to perturbations of f. The perturbations ...
Universal Completability, Least Eigenvalue Frameworks, and Vector Colorings [0.03%]
通用完备性，最小特征值框架和向量着色
Chris Godsil,David E Roberson,Brendan Rooney et al.
Chris Godsil et al.
An embedding i ↦ p i ∈ R d of the vertices of a graph G is called universally completable if the following holds: For any other embedding i ↦ q i ∈ R k satisfying q i T q j = p i T p j for i = j and i adjace...
Bruno Federici,Agelos Georgakopoulos
Bruno Federici
The aim of this paper is to clarify the relationship between Gromov-hyperbolicity and amenability for planar maps. Keywords: ...
A General Framework for Tilings, Delone Sets, Functions, and Measures and Their Interrelation [0.03%]
平铺、德尔昂集、函数和测度及其相互关系的通用框架
Yasushi Nagai
Yasushi Nagai
We define a general framework that includes objects such as tilings, Delone sets, functions, and measures. We define local derivability and mutual local derivability (MLD) between any two of these objects in order to describe their interrel...
Herbert Edelsbrunner,Anton Nikitenko
Herbert Edelsbrunner
The order-k Voronoi tessellation of a locally finite set X ⊆ R n decomposes R n into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas f...
Joshua Cruz,Chad Giusti,Vladimir Itskov et al.
Joshua Cruz et al.
Neural codes serve as a language for neurons in the brain. Open (or closed) convex codes, which arise from the pattern of intersections of collections of open (or closed) convex sets in Euclidean space, are of particular relevance to neuros...
Michael Kerber,Hannah Schreiber
Michael Kerber
A tower is a sequence of simplicial complexes connected by simplicial maps. We show how to compute a filtration, a sequence of nested simplicial complexes, with the same persistent barcode as the tower. Our approach is based on the coning s...