A universality theorem for stressable graphs in the plane
| Autor: | Gaiane Panina |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Algebra and Number Theory
Universality theorem Graph Theoretical Computer Science Universality (dynamical systems) Combinatorics Oriented matroid Hyperplane Grassmannian Convex polytope FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Geometry and Topology Combinatorics (math.CO) Mathematics::Representation Theory Mathematics |
| Popis: | Universality theorems (in the sense of N. Mn\"{e}v) claim that the realization space of a combinatorial object (a point configuration, a hyperplane arrangement, a convex polytope, etc.) can be arbitrarily complicated. In the paper, we prove a universality theorem for a graph in the plane with a prescribed \textit{oriented matroid of stresses}, that is the collection of signs of all possible equilibrium stresses of the graph. This research is motivated by the Grassmanian stratification (Gelfand, Goresky, MacPherson, Serganova) by thin Schubert cells, and by a recent series of papers on stratifications of configuration spaces of tensegrities (Doray, Karpenkov, Schepers, Servatius). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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