### Abstract

Let [n] denote the n-set {1, 2,..., n}, let k, l ≥ 1 be integers. Define f_{l}(n, k) as the minimum number f such that for every family F ⊆ 2^{[n]} with {divides}F{divides}>f, for every k-coloring of [n], there exists a chain A_{1}{subset not double equals}···{subset not double equals}A_{l+1} in F in which the set of added elements, A_{l+1}-A_{1}, is monochromatic. We survey the known results for l = 1. Applying them we prove for any fixed l that there exists a constant φ{symbol}_{l}(k) such that as n→^{∞} f_{l}(n,k)∼φ{symbol}_{l}(k)⌊ 1 2n⌋^{n} and φ{symbol}_{l}(k)∼ φk 4logk as k→^{∞}. Several problems remain open.

Original language | English |
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Pages (from-to) | 143-152 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 63 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 1987 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Füredi, Z., Griggs, J. R., Odlyzko, A. M., & Shearer, J. B. (1987). Ramsey-Sperner theory.

*Discrete Mathematics*,*63*(2-3), 143-152. https://doi.org/10.1016/0012-365X(87)90004-5