Extremal problems in discrete geometry

@article{Szemerdi1983ExtremalPI,
  title={Extremal problems in discrete geometry},
  author={Endre Szemer{\'e}di and William T. Trotter},
  journal={Combinatorica},
  year={1983},
  volume={3},
  pages={381-392}
}
In this paper, we establish several theorems involving configurations of points and lines in the Euclidean plane. Our results answer questions and settle conjectures of P. Erd6s, G. Purdy, and G. Dirac. The principal result is that there exists an absolute constant cl so that wlaen V'n<=t~_[T], the number of incidences between n points and t lines is less than c~n~/3t ""/3. Using this restllt, it follows immediately that there exists an absolute constant c2 so that if k -< ]/~, then the number… CONTINUE READING
BETA

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.

582 Citations

0204060'85'92'00'08'16
Citations per Year
Semantic Scholar estimates that this publication has 582 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
SHOWING 1-4 OF 4 REFERENCES

Some combinatorial problems in geometry, Caltfi, rence held in Haifa, Israel

  • P. ERDOS
  • Lecture Notes in Mathematics,
  • 1979
Highly Influential
6 Excerpts

Similar Papers

Loading similar papers…