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Posets :: isRanked

isRanked -- determines if a poset is ranked

Synopsis

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.

See also

Ways to use isRanked :