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 |
The object hibiIdeal is a method function with options.