# On Ramsey numbers for sets free of prescribed differences

Bruce M. Landman, James T. Perconti

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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) 11-20 10 Journal of Combinatorial Mathematics and Combinatorial Computing 76 Published - Feb 1 2011

Ramsey number
Integer
Colouring

### Keywords

• Difference-free sets
• Integer ramsey theory
• Monochromatic sets

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

On Ramsey numbers for sets free of prescribed differences. / Landman, Bruce M.; Perconti, James T.

In: Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 76, 01.02.2011, p. 11-20.

Research output: Contribution to journalArticle

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