# rankFunction -- computes the rank function of a ranked poset

## Synopsis

• Usage:
rk = rankFunction P
• Inputs:
• P, an instance of the type Poset,
• Outputs:
• rk, a list, such that entry $i$ is the rank of the $i$th member of the ground set

## 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 one such ranking function.

 i1 : (chain 5).GroundSet o1 = {1, 2, 3, 4, 5} o1 : List i2 : rankFunction chain 5 o2 = {0, 1, 2, 3, 4} o2 : List i3 : (booleanLattice 3).GroundSet o3 = {000, 001, 010, 011, 100, 101, 110, 111} o3 : List i4 : rankFunction booleanLattice 3 o4 = {0, 1, 1, 2, 1, 2, 2, 3} o4 : List

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