Macaulay2 » Documentation
Packages » Posets :: flaghPolynomial

next | previous | forward | backward | up | index | toc

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

See also

flagChains -- computes the maximal chains in a list of flags of a ranked poset
flagfPolynomial -- computes the flag-f polynomial of a ranked poset
isRanked -- determines if a poset is ranked

Ways to use flaghPolynomial :

flaghPolynomial(Poset)

For the programmer

The object flaghPolynomial is a method function with options.