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COMPGEOM
1996
ACM

On the Number of Arrangements of Pseudolines

10 years 5 months ago
On the Number of Arrangements of Pseudolines
Given a simple arrangementof n pseudolines in the Euclidean plane, associate with line i the list i of the lines crossing i in the order of the crossings on line i. i = ( i 1; i 2;::; i n?1) is a permutation of f1;::;ng? fig. The vector ( 1; 2;:::; n) is an encoding for the arrangement. De ne i j = 1 if i j > i and i j = 0, otherwise. Let i = ( i 1; i 2;::; i n?1), we show that the vector ( 1; 2;:::; n) is already an encoding. We use this encoding to improve the upper bound on the number of arrangements of n pseudolines to 20:6974 n 2 . Moreover, we have enumerated arrangements with 10 pseudolines. As a by-product we determine their exact number and we can show that the maximal number of halving lines of 10 point in the plane is 13.
Stefan Felsner
Added 08 Aug 2010
Updated 08 Aug 2010
Type Conference
Year 1996
Where COMPGEOM
Authors Stefan Felsner
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