An upper bound for van der Waerden-like numbers using k colors

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3 Scopus citations

Abstract

Functions analogous to the van der Waerden numbers w(n, k) are considered. We replace the class of arithmetic progressions, A, by a class A′, with A ⊂A′; thus, the associated van der Waerden-like number will be smaller for si’. We consider increasing sequences of positive integers x1,…, xn which are either arithmetic progressions or for which there exists a polynomial φ(x) with integer coefficients satisfying φ(xi) = xi+1, i = 1,…, n - 1. Various further restrictions are placed on the types of polynomials allowed. Upper bounds are given for the corresponding functions w′(n, k) for the general pair (n, k). A table of several new computer-generated values of these functions is provided.

Original languageEnglish (US)
Pages (from-to)177-184
Number of pages8
JournalGraphs and Combinatorics
Volume9
Issue number2
DOIs
StatePublished - Jan 1 1993
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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