Resolutions of square-free monomial ideals via facet ideals: a survey

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We survey some recent results on the minimal graded free resolution of a square-free monomial ideal. The theme uniting these results is the point-of-view that the generators of a monomial ideal correspond to the maximal faces (the facets) of a simplicial complex Δ.
26 pages; revised final version to appear in Contemporary Math; updated references

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