Almost complete intersections and Stanley's conjecture

Abstract

Let K be a field and I a monomial ideal of the polynomial ring S = K[x₁, ..., x_n]. We show that if either: 1) I is almost complete intersection, 2) I can be generated by less than four monomials; or 3) I is the Stanley-Reisner ideal of a locally complete intersection simplicial complex on [n], then Stanley's conjecture holds for S/I.