Abstract
We express the multigraded Betti numbers of monomial ideals in four variables in terms of the multigraded Betti numbers of 66 squarefree monomial ideals, also in four variables. We use this class of 66 ideals to prove that monomial resolutions in four variables are independent of the base field. In addition, we give a formula for the Betti numbers of an arbitrary monomial ideal in four variables.
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