Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients

Andreea I. Bordianu, Mircea Cimpoeas

We prove that if $I$ is a monomial ideal with linear quotients in a ring of polynomials $S$ in $n$ indeterminates and $\mathrm{depth}(S/I)=n-2$, then $\operatorname{sdepth}(S…