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 |