# flaghPolynomial -- computes the flag-h polynomial of a ranked poset

## Synopsis

• Usage:
fh = flaghPolynomial P
fh = flaghPolynomial(P, VariableName => symbol)
• Inputs:
• P, an instance of the type Poset, a ranked poset
• Optional inputs:
• VariableName => , default value q
• Outputs:
• fh, , the flag-h polynomial of $P$

## Description

Suppose $f$ is the flagfPolynomial of $P$. The flag-h polynomial of $P$ is the polynomial $(1-q_0)\cdots(1-q_r)f(q_0/(1-q_0), \ldots, q_r/(1-q_r))$.

 i1 : flaghPolynomial booleanLattice 3 o1 = q q + 2q + 2q + 1 1 2 1 2 o1 : ZZ[q ..q ] 0 3

The flag-h polynomial of the $n$ chain is $1$.

 i2 : flaghPolynomial chain 5 o2 = 1 o2 : ZZ[q ..q ] 0 4