Macaulay2 » Documentation
Packages » Posets :: hPolynomial

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

hPolynomial -- computes the h-polynomial of a poset

Synopsis

Usage:

h = hPolynomial P

h = hPolynomial(P, VariableName => symbol)
Inputs:
- P, an instance of the type Poset,
Optional inputs:
- VariableName => a symbol, default value q
Outputs:
- h, a ring element, the h-polynomial of $P$

Description

Suppose $f$ is the fPolynomial of $P$, and $d$ is the degree of $f$. Then the h-polynomial of $P$ is the polynomial $(1-q)^d f(q/(1-q))$.

i1 : hPolynomial booleanLattice 3

      2
o1 = q  + 4q + 1

o1 : ZZ[q]

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

i2 : hPolynomial chain 5

o2 = 1

o2 : ZZ[q]

See also

chains -- computes all chains of a poset
fPolynomial -- computes the f-polynomial of a poset

Ways to use hPolynomial :

hPolynomial(Poset)

For the programmer

The object hPolynomial is a method function with options.