# pure poset

A poset is *pure* if it is finite and every maximal chain has the same length.
If P is a pure poset, we can create a rank function r on P by defining
r(x) to be the length of a maximal chain bounded above by x. Every
interval of a pure poset is a graded poset, and every graded poset is pure. Moreover,
the closure of a pure poset, formed by adjoining an artificial minimum element and
an artificial maximum element, is always graded.

The face poset of a pure simplicial complex is pure as a poset.

Title | pure poset |
---|---|

Canonical name | PurePoset |

Date of creation | 2013-03-22 17:19:47 |

Last modified on | 2013-03-22 17:19:47 |

Owner | mps (409) |

Last modified by | mps (409) |

Numerical id | 4 |

Author | mps (409) |

Entry type | Definition |

Classification | msc 06A06 |