Zobrazeno 1 - 10
of 165
pro vyhledávání: '"GOAOC, XAVIER"'
We introduce and study a notion of decomposition of planar point sets (or rather of their chirotopes) as trees decorated by smaller chirotopes. This decomposition is based on the concept of mutually avoiding sets (which we rephrase as \emph{modules})
Externí odkaz:
http://arxiv.org/abs/2403.10311
We prove that for any set $F$ of $n\ge 2$ pairwise disjoint open convex sets in $\mathbb{R}^3$, the connected components of the set of lines intersecting every member of $F$ are contractible. The same result holds for directed lines.
Comment: Th
Comment: Th
Externí odkaz:
http://arxiv.org/abs/2205.14681
We prove that there exist no weak $\varepsilon$-nets of constant size for lines and convex sets in $\mathbb{R}^d$.
Comment: Boris Bukh has informed us that our construction can be extended to 2-flats in $\mathbb{R}^4$. The contents of this manus
Comment: Boris Bukh has informed us that our construction can be extended to 2-flats in $\mathbb{R}^4$. The contents of this manus
Externí odkaz:
http://arxiv.org/abs/2202.02719
In this paper we study generalizations of classical results on intersection patterns of set systems in $\mathbb{R}^d$, such as the fractional Helly theorem or the $(p,q)$-theorem, in the setting of arbitrary triangulable spaces with a forbidden homol
Externí odkaz:
http://arxiv.org/abs/2103.09286
Autor:
GOAOC, XAVIER1 xavier.goaoc@loria.fr, WELZL, EMO2 emo@inf.ethz.ch
Publikováno v:
Journal of the ACM. Feb2023, Vol. 70 Issue 1, p1-47. 47p.
Autor:
Goaoc, Xavier, Welzl, Emo
We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of rank $3$): (a) The number of extreme points in an $n$-point o
Externí odkaz:
http://arxiv.org/abs/2003.08456
We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in $\mathbb{R}^3$. We show that this question, which is equivalent to deciding the emptiness of certain semi-algebrai
Externí odkaz:
http://arxiv.org/abs/1903.03014
Publikováno v:
Annales Henri Lebesgue 3 (2020), 701-715
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for the uniform
Externí odkaz:
http://arxiv.org/abs/1902.06519
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently the space
Externí odkaz:
http://arxiv.org/abs/1812.08525
Autor:
Goaoc, Xavier, Hubard, Alfredo, de Verclos, Rémi de Joannis, Sereni, Jean-Sébastien, Volec, Jan
We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding the minim
Externí odkaz:
http://arxiv.org/abs/1811.02236