### 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 1 2011 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'On Ramsey numbers for sets free of prescribed differences'. Together they form a unique fingerprint.

## Cite this

Landman, B. M., & Perconti, J. T. (2011). On Ramsey numbers for sets free of prescribed differences.

*Journal of Combinatorial Mathematics and Combinatorial Computing*,*76*, 11-20.