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.

Ways to use rankFunction :

rankFunction(Poset)

For the programmer

The object rankFunction is a method function.

rankFunction -- computes the rank function of a ranked poset

Synopsis

Description

See also

Ways to use rankFunction :

For the programmer