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