Graded poset

In mathematics, in the branch of combinatorics, a graded poset is a partially ordered set (poset) P equipped with a rank function ρ from P to N satisfying the following two properties:

The value of the rank function for an element of the poset is called its rank. Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see ranked poset. A rank or rank level of a graded poset is the subset of all the elements of the poset that have a given rank value.

Graded posets play an important role in combinatorics and can be visualized by means of a Hasse diagram.

Examples

Some examples of graded posets (with the rank function in parentheses) are: