The Szemerédi-Trotter theorem in the complex plane

The Szemerédi-Trotter theorem in the complex plane

It is shown that n points and e lines in the complex Euclidean plane ℂ 2 determine O ( n 2/3 e 2/3 + n + e ) point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemerédi and Trotter about point-line incidences in the real Euclidean plane ℝ 2 .

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Veröffentlicht in:Combinatorica (Budapest. 1981) 2015-02, Vol.35 (1), p.95-126
1. Verfasser: Tóth, Csaba D.
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung:It is shown that n points and e lines in the complex Euclidean plane ℂ 2 determine O ( n 2/3 e 2/3 + n + e ) point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemerédi and Trotter about point-line incidences in the real Euclidean plane ℝ 2 .
ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-014-2686-2