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 => a symbol, default value q
Outputs:
- ff, a ring element, 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

Ways to use flagfPolynomial :

flagfPolynomial(Poset)

For the programmer

The object flagfPolynomial is a method function with options.

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

Synopsis

Description

See also

Ways to use flagfPolynomial :

For the programmer