Zobrazeno 1 - 10
of 100
pro vyhledávání: '"Sandoval, Leonardo"'
In this note we study a conjecture by Jer\'onimo-Castro, Magazinov and Sober\'on which generalized a question posed by Dol'nikov. Let $F_1,F_2,\dots,F_n$ be families of translates of a convex compact set $K$ in the plane so that each two sets from di
Externí odkaz:
http://arxiv.org/abs/2307.07714
Autor:
Pacheco-Sandoval, Leonardo1,2 Lpacheco560@unab.edu.co, Alirio Díaz-González, Carlos1,2, David Acebedo-Roncancio, Germán1,2, Ángel Rodríguez-Camacho, Miguel1,2
Publikováno v:
Revista Facultad de Ingeniería Universidad de Antioquia. Oct-Dec2024, Issue 113, p19-27. 9p.
Publikováno v:
In Sustainable Cities and Society 15 December 2024 117
We show that any total preorder on a set with $\binom{n}{2}$ elements coincides with the order on pairwise distances of some point collection of size $n$ in $\mathbb{R}^{n-1}$. For linear orders, a collection of $n$ points in $\mathbb{R}^{n-2}$ suffi
Externí odkaz:
http://arxiv.org/abs/2111.08895
Autor:
Flores-Peñaloza, David, Kano, Mikio, Martínez-Sandoval, Leonardo, Orden, David, Tejel, Javier, Tóth, Csaba D., Urrutia, Jorge, Vogtenhuber, Birgit
Publikováno v:
Discrete Mathematics 344(7) (2021), 112406
Given a colored point set in the plane, a perfect rainbow polygon is a simple polygon that contains exactly one point of each color, either in its interior or on its boundary. Let $\operatorname{rb-index}(S)$ denote the smallest size of a perfect rai
Externí odkaz:
http://arxiv.org/abs/2007.10139
Let $P$ be a set of points in $\mathbb{R}^d$, $B$ a bicoloring of $P$ and $\Oo$ a family of geometric objects (that is, intervals, boxes, balls, etc). An object from $\Oo$ is called balanced with respect to $B$ if it contains the same number of point
Externí odkaz:
http://arxiv.org/abs/2002.05488
Publikováno v:
Journal of Combinatorial Theory, Series B. Volume 149, 2021, pp. 23-51
The convex dimension of a $k$-uniform hypergraph is the smallest dimension $d$ for which there is an injective mapping of its vertices into $\mathbb{R}^d$ such that the set of $k$-barycenters of all hyperedges is in convex position. We completely det
Externí odkaz:
http://arxiv.org/abs/1909.01189
A widely investigated subject in combinatorial geometry, originated from Erd\H{o}s, is the following. Given a point set $P$ of cardinality $n$ in the plane, how can we describe the distribution of the determined distances? This has been generalized i
Externí odkaz:
http://arxiv.org/abs/1902.03166
Publikováno v:
In Engineering Structures 15 February 2023 277
Let $\mathcal{F}$ be a family of convex sets in ${\mathbb R}^d$, which are colored with $d+1$ colors. We say that $\mathcal{F}$ satisfies the Colorful Helly Property if every rainbow selection of $d+1$ sets, one set from each color class, has a non-e
Externí odkaz:
http://arxiv.org/abs/1803.06229