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Line arrangements with the maximal number of triple points. (English) Zbl 1333.52026

Summary: The purpose of this note is to study configurations of lines in projective planes over arbitrary fields having the maximal number of intersection points where three lines meet. We give precise conditions on ground fields \(\mathbb F\) over which such extremal configurations exist. We show that there does not exist a field admitting a configuration of 11 lines with 17 triple points, even though such a configuration is allowed combinatorially. Finally, we present an infinite series of configurations which have a high number of triple intersection points.

MSC:

52C30 Planar arrangements of lines and pseudolines (aspects of discrete geometry)
05B30 Other designs, configurations
14Q10 Computational aspects of algebraic surfaces

Software:

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References:

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