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Posets :: rankGeneratingFunction

rankGeneratingFunction -- computes the rank generating function of a ranked poset

Synopsis

Description

The rank generating function of P is the polynomial with the coefficient of qi given by the number of vertices in rank i of P.

The rank generating function of the n chain is qn-1 + …+ q + 1.

i1 : n = 5;
i2 : rankGeneratingFunction chain n

      4    3    2
o2 = q  + q  + q  + q + 1

o2 : ZZ[q]

The rank generating function of the n booleanLattice is (q+1)n.

i3 : factor rankGeneratingFunction booleanLattice n

            5
o3 = (q + 1)

o3 : Expression of class Product

See also

Ways to use rankGeneratingFunction :