## Abstract

Let 2^{[n]} denote the Boolean lattice of order n, that is, the poset of subsets of {1,...,n} ordered by inclusion. Extending our previous work on a question of Füredi, we show that for any c>1, there exist functions e(n)∼ n/2 and f(n)∼c nlogn and an integer N (depending only on c) such that for all n>N, there is a chain decomposition of the Boolean lattice 2^{[n]} into (_{⌊n/2⌋} ^{n} chains, all of which have size between e(n) and f(n). (A positive answer to Füredi's question would imply that the same result holds for some e(n)∼ π/2 n and f(n)=e(n)+1.) The main tool used is an apparently new observation about rank-collection in normalized matching (LYM) posets.

Original language | English (US) |
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Pages (from-to) | 219-228 |

Number of pages | 10 |

Journal | European Journal of Combinatorics |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2003 |

## Keywords

- Boolean lattice
- Chain decompositions
- Füredi's problem
- LYM property
- Normalized matching property