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

Synopsis

Usage:
L = rankPoset P
Inputs:
- P, an object of class Poset
Outputs:
- L, a list, containing lists such that the ith list is the set of vertices in the ith 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)

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

Synopsis

Description

See also

Ways to use rankPoset :

Ways to use `rankPoset` :