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Posets :: hibiIdeal

hibiIdeal -- produces the Hibi ideal of a poset

Synopsis

Description

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

See also

Ways to use hibiIdeal :