## A van der Waerden Variant

- Kevin J. Compton
- Electr. J. Comb.
- 1999

@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} }

- Published 1988 in Discrete Mathematics
DOI:10.1016/0012-365X(88)90043-X

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