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fPolynomial -- computes the f-polynomial of a poset

Synopsis

Usage:

f = fPolynomial P

f = fPolynomial(P, VariableName => symbol)
Inputs:
- P, an instance of the type Poset,
Optional inputs:
- VariableName => a symbol, default value q
Outputs:
- f, a ring element, the f-polynomial of $P$

Description

The f-polynomial of $P$ is the polynomial such that the coefficient on $q^i$ is the number of chains of length $i$ in $P$.

The f-polynomial of the $n$ chain is $(q+1)^n$.

i1 : n = 5;

i2 : factor fPolynomial chain n

            5
o2 = (q + 1)

o2 : Expression of class Product

See also

chains -- computes all chains of a poset
hPolynomial -- computes the h-polynomial of a poset

Ways to use fPolynomial :

fPolynomial(Poset)

For the programmer

The object fPolynomial is a method function with options.