  We study two partial orders on $[x_1,...,x_n]$, the free abelian monoid on
${x_1,...,x_n}$. These partial orders, which we call the ``strongly stable''
and the ``stable'' partial order, are defined by the property that their
filters are precisely the strongly stable and the stable monoid ideals. These
ideals arise in the study of generic initial ideals.
