Some Classes of Monomial Ideals with Linear Quotients

Monomial ideals are at the intersection of commutative algebra and combinatorics. Many important problems in polynomial rings can be reduced to the study of monomial ideals. To squarefree monomial ideals, one may attach simplicial complexes and vice versa. Namely, with any simplicial complex one may associate a squarefree monomial ideal, generated by the squarefree monomials corresponding to the minimal non-faces of the simplicial complex. On one hand, this allows the study of simplicial complexes by algebraic methods.