On Ramsey numbers for sets free of prescribed differences

Bruce M. Landman; James T. Perconti

On Ramsey numbers for sets free of prescribed differences

Bruce M. Landman, James T. Perconti

Research output: Contribution to journal › Article › peer-review

Abstract

For a positive integer d, a set S of positive integers is difference d-tree if \x-y\ # d for all x, y ε S. We consider the following Ramseytheoretical question: Given d, k, r ε Z⁺, what is the smallest integer n such that every r-coloring of [1, n] contains a monochromatic k-element difference d-free set? We provide a formula for this n. We then consider the more general problem where the monochromatic fc-element set must avoid a given set of differences rather than just one difference.

Original language	English (US)
Pages (from-to)	11-20
Number of pages	10
Journal	Journal of Combinatorial Mathematics and Combinatorial Computing
Volume	76
State	Published - Feb 2011
Externally published	Yes

Keywords

Difference-free sets
Integer ramsey theory
Monochromatic sets

ASJC Scopus subject areas

General Mathematics

Cite this

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AB - For a positive integer d, a set S of positive integers is difference d-tree if \x-y\ # d for all x, y ε S. We consider the following Ramseytheoretical question: Given d, k, r ε Z+, what is the smallest integer n such that every r-coloring of [1, n] contains a monochromatic k-element difference d-free set? We provide a formula for this n. We then consider the more general problem where the monochromatic fc-element set must avoid a given set of differences rather than just one difference.

KW - Difference-free sets

KW - Integer ramsey theory

KW - Monochromatic sets

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On Ramsey numbers for sets free of prescribed differences

Abstract

Keywords

ASJC Scopus subject areas

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Cite this