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
Highly Influential
This paper has highly influenced 51 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.

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
1 Excerpt

Similar Papers

Loading similar papers…