Values and bounds for Ramsey numbers associated with polynomial iteration

  title={Values and bounds for Ramsey numbers associated with polynomial iteration},
  author={Bruce M. Landman and Raymond N. Greenwell},
  journal={Discrete Mathematics},
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

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Iwo combinatorial theorems on arithmetic progressions

  • W. M. Schmidt
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