## Abstract

Stanley used the Aleksandrov-Fenchel inequalities from the theory of mixed volumes to prove the following results. Let P be a partially ordered set with n elements, and let x ε{lunate} P, If N
_{i}
^{*} is the number of linear extension λ : P → {1, 2, ..., n} satisfying λ(x) = i, then the sequence N
_{1}
^{*}, ..., N
_{n}
^{*} is log concave (and therefore unimodal). Here the analogous results for both strict order-preserving and order-preserving maps are proved using an explicit injection. Further, if ν
_{c} is the number of strict order-preserving maps of P into a chain of length c, then ν
_{c} is shown to be log concave, and the corresponding result is established for order-preserving maps.

Original language | English |
---|---|

Pages (from-to) | 221-226 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 50 |

Issue number | C |

DOIs | |

Publication status | Published - 1984 |

Externally published | Yes |