# rankPoset -- generates a list of lists representing the ranks of a ranked poset

## Synopsis

• Usage:
L = rankPoset P
L = rank Poset
• Inputs:
• P, an instance of the type Poset,
• Outputs:
• L, a list, containing lists such that the $i$th list is the set of vertices in the $i$th rank of $P$

## Description

The poset $P$ is ranked if there exists an integer function $r$ on the vertex set of $P$ such that for each $a$ and $b$ in the poset if $b$ covers $a$ then $r(b) - r(a) = 1$.

This method returns the list of vertices in each rank.

 i1 : rankPoset chain 5 o1 = {{1}, {2}, {3}, {4}, {5}} o1 : List i2 : rankPoset booleanLattice 3 o2 = {{000}, {001, 010, 100}, {011, 101, 110}, {111}} o2 : List

This method uses the method rankFunction, which was ported from John Stembridge's Maple package available at http://www.math.lsa.umich.edu/~jrs/maple.html#posets.