General Position for Planar Line Arrangements and $HD_2(p,3)$
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Statement
For every and infinitely many there is a set of lines in the plane with no intersecting quadruple such that every subset of size at least contains three concurrent lines. This improves the bound for a dual form of a theorem of Balogh and Solymosi, and yields an improved lower bound for the Hadwiger-Debrunner number .
Context
improved bounds; the exact Hadwiger-Debrunner numbers remain open
Hadwiger-Debrunner numbers sit in the classical (p,q)-problem tradition solved by Alon and Kleitman, and their growth rates are actively tracked in discrete geometry.
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improved bounds; the exact Hadwiger-Debrunner numbers remain open
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