| Autor: |
Chatzikonstantinou, N., Iosevich, A., Mkrtchyan, S., Pakianathan, J. |
| Rok vydání: |
2017 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
For a compact set $E \subset \mathbb R^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k+1$ points in $E$ such that the distance between a pair of points is specified if the corresponding vertices of $G$ are connected by an edge. We regard two such frameworks as equivalent if the specified distances are the same. We show that in a suitable sense the set of equivalences of such frameworks naturally embeds in ${\mathbb R}^m$ where $m$ is the number of "essential" edges of $G$. We prove that there exists a threshold $s_k
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| Databáze: |
arXiv |
| Externí odkaz: |
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