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.

Ways to use rankPoset :

rankPoset(Poset)

For the programmer

The object rankPoset is a method function.

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

Synopsis

Description

See also

Ways to use rankPoset :

For the programmer