isRanked -- determines if a poset is ranked

Synopsis

Usage:

i = isRanked P
Inputs:
- P, an instance of the type Poset,
Outputs:
- i, a Boolean value, whether $P$ is ranked

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 $r(b) - r(a) = 1$.

The $n$ chain and the $n$ booleanLattice are ranked.

i1 : n = 5;

i2 : C = chain n;

i3 : isRanked C

o3 = true

i4 : rankFunction C

o4 = {0, 1, 2, 3, 4}

o4 : List

i5 : B = booleanLattice n;

i6 : isRanked B

o6 = true

i7 : rankGeneratingFunction C

      4    3    2
o7 = q  + q  + q  + q + 1

o7 : ZZ[q]

However, the pentagon lattice is not ranked.

i8 : P = poset {{1,2}, {1,3}, {3,4}, {2,5}, {4,5}};

i9 : isRanked P

o9 = false

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

Ways to use isRanked :

isRanked(Poset)

For the programmer

The object isRanked is a method function.

isRanked -- determines if a poset is ranked

Synopsis

Description

See also

Ways to use isRanked :

For the programmer