Almost complete intersections and Stanley's conjecture

Abstract

Let $K$ be a field and $I$ a monomial ideal of the polynomial ring $S=K[x_1,\dots ,x_n]$. 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 $S/I$.

To appear in Kodai Mathematical Journal, 7 pages

References in corpus (2)

• Stanley depth of monomial ideals with small number of generators
• The Stanley conjecture on monomial almost complete intersection ideals