Values and bounds for Ramsey numbers associated with polynomial iteration

@article{Landman1988ValuesAB,
  title={Values and bounds for Ramsey numbers associated with polynomial iteration},
  author={Bruce M. Landman and Raymond N. Greenwell},
  journal={Discrete Mathematics},
  year={1988},
  volume={68},
  pages={77-83}
}
Ramsey numbers similar to those of van der Waerden are examined. Rather than considering arithmetic sequences, we look at increasing sequences of positive integers {x1, x2, l l l I x,,} for which there exists a polynomial f(x) = &,aixi, with a, E 2 and Xj+l =f(Xj). We denote by p,(n) the least positive integer such that if [I, 2, . . . , p,(n)] is 2=colored, then there exists a monochromatic sequence of length n generated by a polynomial of degree SC We give values for p,(n) for n s 5, as well… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-3 of 3 references

Iwo combinatorial theorems on arithmetic progressions

  • W. M. Schmidt
  • Generalized van der Waerden numbers , Graphs and…
  • 1986

Similar Papers

Loading similar papers…