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.
|Date of creation||2013-03-22 17:19:47|
|Last modified on||2013-03-22 17:19:47|
|Last modified by||mps (409)|