In mathematics, in the branch of combinatorics, a graded poset, sometimes called a ranked poset (but see the article for an alternative meaning), is a partially ordered set (poset) P equipped with a rank function ρ from P to N compatible with the ordering (so ρ(x)<ρ(y) whenever x < y) such that whenever y covers x, then . The value of the rank function for an element of the poset is called its rank.
Sometimes the term rank refers to a subset of all elements of the poset which have the same rank value. To avoid the confusion sometimes the term rank level is used for this purpose.
Graded posets play an important role in combinatorics and can be visualized by means of a Hasse diagram.
Read more about Graded Poset: Examples, Alternative Characterizations, The Usual Case
Famous quotes containing the word graded:
“I don’t want to be graded on a curve.”
—Mary Carillo (b. 1957)