Let $\mathbb{ K}$ be a field, and let $S=\mathbb{ K}[X_1, ..., X_n]$ be the polynomial ring. Let $I$ be a monomial ideal of $S$ with up to 5 generators. In this paper, we present a computational experiment which allows us to prove that $\mathrm{ depth}_S S/I = \mathrm{ sdepth}_S S/I < \mathrm{ sdepth}_S I$. This shows that the Stanley conjecture is true for $S/I$ and $I$, if $I$ can be generated by at most 5 monomials. The result also brings additional computational evidence for a conjecture made by Herzog.
Categories: math.AC