Some new bounds and values for van der Waerden-like numbers

Bruce M. Landman, Raymond N. Greenwell

Research output: Contribution to journalArticlepeer-review


Numbers similar to those of van der Waerden are studied. We consider increasing sequences of positive integers {x1, x2,..., xn} that either form an arithmetic progression or for which there exists a polynomial f with integer coefficients and degree exactly n - 2, and xj+1 =f(xj). We denote by q(n, k) the least positive integer such that if {1, 2,..., q(n, k)} is partitioned into k classes, then some class must contain a sequence of the type just described. Upper bounds are obtained for q(n, 3), q(n, 4), q(3, k), and q(4, k). A table of several values is also given.

Original languageEnglish (US)
Pages (from-to)287-291
Number of pages5
JournalGraphs and Combinatorics
Issue number3
StatePublished - Sep 1 1990
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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