Ramsey functions related to the van der waerden numbers

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Abstract

Ramsey functions similar to the van der Waerden numbers w(n) are studied. If A' is a class of sequences which includes the n-term arithmetic progressions, then we define w'(n) to be the least positive integer guaranteeing that if {1,2,...,w'(n)} is 2-colored, then there exists a monochromatic member of A'. We consider increasing sequences of positive integers {x1,...,xn} which are either arithmetic progressions or for which there exists a polynomial p(x) with integer coefficients satisfying p(xi) = xi+1. Various further restrictions are placed on the types of polynomials allowed. Upper bounds are given for the corresponding functions w'(n). In addition, it is shown that the existence of somewhat stronger bounds on w'(n) would imply similar bounds for w(n).

Original languageEnglish (US)
Pages (from-to)265-278
Number of pages14
JournalDiscrete Mathematics
Volume102
Issue number3
DOIs
StatePublished - May 22 1992

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Arithmetic sequence
Polynomials
Integer
Polynomial
Monotonic increasing sequence
Upper bound
Restriction
Imply
Coefficient
Term
Class

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Ramsey functions related to the van der waerden numbers. / Landman, Bruce M.

In: Discrete Mathematics, Vol. 102, No. 3, 22.05.1992, p. 265-278.

Research output: Contribution to journalArticle

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