# 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 => , default value q
• Outputs:
• f, , 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

• 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 .