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

Synopsis

• Usage:

  r = rankGeneratingFunction P

  r = rankGeneratingFunction(P, VariableName => symbol)

• Inputs:
  • P, an instance of the type Poset, a ranked poset
• Optional inputs:
  • VariableName => a symbol
• Outputs:
  • r, a ring element, the rank generating function of P

Description

i1 : n = 5;

i2 : rankGeneratingFunction chain n

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

o2 : ZZ[q]

i3 : factor rankGeneratingFunction booleanLattice n

            5
o3 = (q + 1)

o3 : Expression of class Product

See also

• isRanked -- determines if a poset is ranked
• rankPoset -- generates a list of lists representing the ranks of a ranked poset