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Classification theorem for strong triangle blocking arrangements
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abstract
A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. Our aim in this paper is to prove a classification theorem for strong triangle blocking arrangements. As an application, we obtain a new proof of the result of Ackerman, Buchin, Knauer, Pinchasi and Rote which says that $n$ points in general position cannot be blocked by $n-1$ points, unless $n = 2,4$. We also conjecture an extremal variant of the blocking points problem.
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Cited by 1 Pith paper
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On sets of $n$ points in general position that determine lines that can be pierced by $n$ points
Under an outside-segment piercing condition, any n-point general-position set together with its n piercing points is contained in a cubic curve.
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