Zobrazeno 1 - 10
of 86
pro vyhledávání: '"Dewar, Sean"'
Autor:
Clinch, Katie, Dewar, Sean, Fuladi, Niloufar, Gorsky, Maximilian, Huynh, Tony, Kastis, Eleftherios, Nixon, Anthony, Servatius, Brigitte
Given a triangulation $G$ of a surface $\mathbb{D}$, a spanning disk is a disk $\mathbb{D} \subseteq \mathbb{S}$ containing all the vertices of $G$ such that the boundary of $\mathbb{D}$ is a cycle of $G$. In this paper, we consider the question of w
Externí odkaz:
http://arxiv.org/abs/2410.04450
We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessary combinatorial condition on graphs with reflection-symmetric flexibl
Externí odkaz:
http://arxiv.org/abs/2408.06928
This article considers the problem of 3-dimensional genome reconstruction for single-cell data, and the uniqueness of such reconstructions in the setting of haploid organisms. We consider multiple graph models as representations of this problem, and
Externí odkaz:
http://arxiv.org/abs/2407.10700
The concept of graph flattenability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces into a given normed space. A finite simple graph $G=(V,E)$ is said to
Externí odkaz:
http://arxiv.org/abs/2405.02189
Autor:
Dewar, Sean, Grasegger, Georg, Nixon, Anthony, Rosen, Zvi, Sims, William, Sitharam, Meera, Urizar, David
Consider a collection of points and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on this set of elements is the well studied 2-dimensional rigidity matroid. This article analyzes a cons
Externí odkaz:
http://arxiv.org/abs/2403.16145
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the extremal
Externí odkaz:
http://arxiv.org/abs/2403.00655
We explore the rigidity of generic frameworks in 3-dimensions whose underlying graph is close to being planar. Specifically we consider apex graphs, edge-apex graphs and their variants and prove independence results in the generic 3-dimensional rigid
Externí odkaz:
http://arxiv.org/abs/2402.17499
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity. We then c
Externí odkaz:
http://arxiv.org/abs/2402.14093
Autor:
Dewar, Sean, Grasegger, Georg
A graph is $d$-rigid if for any generic realisation of the graph in $\mathbb{R}^d$ (equivalently, the $d$-dimensional sphere $\mathbb{S}^d$), there are only finitely many non-congruent realisations in the same space with the same edge lengths. By ext
Externí odkaz:
http://arxiv.org/abs/2309.16416
In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit $d$-spheres that may touch but not overlap. Given the existence of such a collection, one may analyse the contact graph
Externí odkaz:
http://arxiv.org/abs/2307.03525