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arxiv 2408.09370 v2 pith:C53UT5YB submitted 2024-08-18 math.CO

On Perles' configuration

classification math.CO
keywords coordinatesperlespointsarrangementplanerationalrealizableconfiguration
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In the 60s, Micha Perles constructed a point-line arrangement in the plane on nine points, which can not be realized only by points with rational coordinates. Gr\"unbaum conjectured that Perles' construction is the smallest: any geometric arrangement on eight or fewer points if it is realizable with real coordinates in the plane, it is also realizable with rational coordinates. In this paper, we prove the conjecture.

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