Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Dobbins, Michael Gene"'
The colorful Helly theorem and Tverberg's theorem are fundamental results in discrete geometry. We prove a theorem which interpolates between the two. In particular, we show the following for any integers $d \geq m \geq 1$ and $k$ a prime power. Supp
Externí odkaz:
http://arxiv.org/abs/2403.14909
Autor:
Dobbins, Michael Gene, Lee, Seunghun
We call an order type inscribable if it is realized by a point configuration where the extreme points are all on a circle. In this paper, we investigate inscribability of order types. We first show that every simple order type with at most 2 interior
Externí odkaz:
http://arxiv.org/abs/2206.01253
Motivated from the surrounding property of a point set in $\mathbb{R}^d$ introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simplicial sphere. As an attempt to give a lower bound for the maximum tra
Externí odkaz:
http://arxiv.org/abs/2111.06560
Autor:
Dobbins, Michael Gene
This is the third paper in a series on oriented matroids and Grassmannians. We construct a $(\mathrm{O}_3\times\mathbb{Z}_2)$-equivariant strong deformation retraction from the homeomorphism group of the 2-sphere to $\mathrm{O}_3$, where the action o
Externí odkaz:
http://arxiv.org/abs/2108.02134
Autor:
Dobbins, Michael Gene
We study the evolution of a Jordan curve on the 2-sphere by curvature flow, also known as curve shortening flow, and by level-set flow, which is a weak formulation of curvature flow. We show that the evolution of the curve depends continuously on the
Externí odkaz:
http://arxiv.org/abs/2106.08907
We prove that the largest convex shape that can be placed inside a given convex shape $Q \subset \mathbb{R}^{d}$ in any desired orientation is the largest inscribed ball of $Q$. The statement is true both when "largest" means "largest volume" and whe
Externí odkaz:
http://arxiv.org/abs/1912.08477
In the Art Gallery Problem we are given a polygon $P\subset [0,L]^2$ on $n$ vertices and a number $k$. We want to find a guard set $G$ of size $k$, such that each point in $P$ is seen by a guard in $G$. Formally, a guard $g$ sees a point $p \in P$ if
Externí odkaz:
http://arxiv.org/abs/1811.01177
Autor:
Dobbins, Michael Gene, Frick, Florian
The first author showed that for a given point $p$ in an $nk$-polytope $P$ there are $n$ points in the $k$-faces of $P$, whose barycenter is $p$. We show that we can increase the dimension of $P$ by $r$, if we allow $r$ of the points to be in $(k+1)$
Externí odkaz:
http://arxiv.org/abs/1809.01613
Autor:
Dobbins, Michael Gene
We extend vector configurations to more general objects that have nicer combinatorial and topological properties, called weighted pseudosphere arrangements. These are defined as a weighted variant of arrangements of pseudospheres, as in the Topologic
Externí odkaz:
http://arxiv.org/abs/1712.09654
A shadow of a geometric object $A$ in a given direction $v$ is the orthogonal projection of $A$ on the hyperplane orthogonal to $v$. We show that any topological embedding of a circle into Euclidean $d$-space can have at most two shadows that are sim
Externí odkaz:
http://arxiv.org/abs/1706.02355