## Abstract

An infinite integer matrix

*A*is called image partition regular if, whenever the natural numbers are finitely coloured, there is an integer vector*x*such that*Ax*is monochromatic. Given an image partition regular matrix*A*, can we also insist that each variable*x*is a multiple of some given_{i}*d*? This is a question of Hindman, Leader and Strauss. Our aim in this short note is to show that the answer is negative. As an application, we disprove a conjectured equivalence between the two main forms of partition regularity, namely image partition regularity and kernel partition regularity._{i}Original language | English |
---|---|

Pages (from-to) | 293-297 |

Number of pages | 5 |

Journal | Journal of Combinatorics |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 |

## Keywords

- partition regular systems
- Ramsey theory