hibiIdeal -- produces the Hibi ideal of a poset

Synopsis

Usage:

H = hibiIdeal P
Inputs:
- P, an instance of the type Poset,
Optional inputs:
- CoefficientRing => a ring, default value QQ, which specifies the coefficient ring of the PolynomialRing $H$ is constructed in
Outputs:
- H, a monomial ideal, the Hibi ideal of $P$

Description

The Hibi ideal of $P$ is a MonomialIdeal built over a ring in $2n$ variables $x_0, \ldots, x_{n-1}, y_0, \ldots, y_{n-1}$, where $n$ is the size of the ground set of $P$. The generators of the ideal are in bijection with order ideals in $P$. Let $I$ be an order ideal of $P$. Then the associated monomial is the product of the $x_i$ associated with members of $I$ and the $y_i$ associated with non-members of $I$.

i1 : hibiIdeal chain 3

o1 = monomialIdeal (x x x , x x y , x y y , y y y )
                     0 1 2   0 1 2   0 1 2   0 1 2

o1 : MonomialIdeal of QQ[x ..x , y ..y ]
                          0   2   0   2

Ways to use hibiIdeal :

hibiIdeal(Poset)

For the programmer

The object hibiIdeal is a method function with options.

hibiIdeal -- produces the Hibi ideal of a poset

Synopsis

Description

See also

Ways to use hibiIdeal :

For the programmer