A Density Version of a Geometric Ramsey Theorem

@article{Brown1982ADV,
  title={A Density Version of a Geometric Ramsey Theorem},
  author={Tom C. Brown and Joe Buhler},
  journal={J. Comb. Theory, Ser. A},
  year={1982},
  volume={32},
  pages={20-34}
}
Let V be an n-dimensional affine space over the field with pd elements, p 6= 2. Then for every ε > 0 there is an n(ε) such that if n = dim(V ) n(ε) then any subset of V with more than εjV j elements must contain 3 collinear points (i.e., 3 points lying in a one-dimensional affine subspace). 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 11 references

On certain sets of integers II

Klaus F. Roth
J. London Math. Soc • 1954
View 6 Excerpts
Highly Influenced

Graham , Rudiments of ramsey theory

L. Ronald
1981

Caps and codes

Discrete Mathematics • 1978
View 3 Excerpts

Roth , On certain sets of integers II

F Klaus
Discrete Math . • 1978

Ramsey's Theorem for a Class of Categories.

Proceedings of the National Academy of Sciences of the United States of America • 1972
View 1 Excerpt

Hales and Robert I . Jewett , Regularity and positional games

W. Alfred
Proc . Symp . Pure Math . • 1971

Ramsey’s theorem for n-parameter

Ronald L. Graham, Bruce L. Rothschild
sets, Trans. Amer. Math. Soc • 1971
View 1 Excerpt

On complete caps and ovaloids in three-dimensional Galois spaces of characteristic 2, Acta Arith

B. Segre
1959
View 2 Excerpts

Spencer , Ramsey ’ s theorem for spaces

H. Joel
Acta Arith . • 1959

Similar Papers

Loading similar papers…