## Abstract

In this paper for t > 2 and n > 2, we give a simple upper bound on a ([t]^{n}), the number of antichains in chain product poset [t]^{n}. When t = 2, the problem reduces to classical Dedekind’s problem posed in 1897 and studied extensively afterwards. However few upper bounds have been proposed for t > 2 and n > 2. The new bound is derived with straightforward extension of bracketing decomposition used by Hansel for bound 3(n⌊n/2⌋) for classical Dedekind’s problem. To our best knowledge, our new bound is the best when Θ((log2t)2)=6t4(log2(t+1))2π(t2−1)(2t−12log2(πt))2<n and t=ω(n1/8(log2n)3/4).

Original language | English |
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Pages (from-to) | 507-510 |

Number of pages | 4 |

Journal | Order |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - 1 Nov 2019 |

## Keywords

- Dedekind’s problem
- Monotonic Boolean function
- Partially ordered set

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