# flagfPolynomial -- computes the flag-f polynomial of a ranked poset

## Synopsis

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

## Description

Suppose $P$ is a rank $r$ poset. For each strictly increasing sequence $(i_1, \ldots, i_k)$ with $0 \leq i_j \leq i_k$, the coefficient of $q_i_1 \cdots q_i_k$ is the number of flagChains in the ranks $i_1, \cdots, i_k$.

The flag-f polynomial of the $n$ chain is $(q_0 + 1)\cdots(q_{n-1}+1)$.

 i1 : n = 4; i2 : factor flagfPolynomial chain n o2 = (q + 1)(q + 1)(q + 1)(q + 1) 3 2 1 0 o2 : Expression of class Product

• flagChains -- computes the maximal chains in a list of flags of a ranked poset
• flaghPolynomial -- computes the flag-h polynomial of a ranked poset
• isRanked -- determines if a poset is ranked

## Ways to use flagfPolynomial :

• "flagfPolynomial(Poset)"

## For the programmer

The object flagfPolynomial is .