The Hibi ideal of P is a MonomialIdeal built over a ring in 2n variables x0, ..., xn-1, y0, ..., yn-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 xi associated with members of I and the yi 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 , x , y , y , y ]
0 1 2 0 1 2