Simplicial complexes and minimal free resolution of monomial algebras
  This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those algebras is related to the combinatorics of some simplicial complexes. Our description may be interpreted as an algorithmic procedure to partially compute this resolution. 
Ignacio Ojeda and A. Vigneron-Tenorio