Values and bounds for Ramsey numbers associated with polynomial iteration

Bruce M. Landman, Raymond N. Greenwell

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

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,...,xn} for which there exists a polynomial {cauchy integral}(x)=∑ri=0aix i, with aiε{lunate}Z and xj+1={cauchy integral}(xj). We denote by pr(n) the least positive integer such that if [1,2,...,pr(n)] is 2-colored, then there exists a monochromatic sequence of length n generated by a polynomial of degree ≤r. We give values for pr(n) for n≤5, as well as lower bounds for p1(n) and p2(n). We also give an upper bound for certain Ramsey numbers that are in between pn-2(n) and the nth van der Waerden number.

Original languageEnglish (US)
Pages (from-to)77-83
Number of pages7
JournalDiscrete Mathematics
Volume68
Issue number1
DOIs
StatePublished - 1988
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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