TY - JOUR AU - Seyed Fakhari, S. A. PY - 2017/02/23 Y2 - 2024/03/29 TI - Stanley depth and symbolic powers of monomial ideals JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 120 IS - 1 SE - Articles DO - 10.7146/math.scand.a-25501 UR - https://www.mscand.dk/article/view/25501 SP - 5-16 AB - <p>The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal $I$ and every pair of integers $k, s\geq 1$, the inequalities $\mathrm{sdepth} (S/I^{(ks)}) \leq \mathrm{sdepth} (S/I^{(s)})$ and $\mathrm{sdepth}(I^{(ks)}) \leq \mathrm{sdepth} (I^{(s)})$ hold. If moreover $I$ is unmixed of height $d$, then we show that for every integer $k\geq1$, $\mathrm{sdepth}(I^{(k+d)})\leq \mathrm{sdepth}(I^{{(k)}})$ and $\mathrm{sdepth}(S/I^{(k+d)})\leq \mathrm{sdepth}(S/I^{{(k)}})$. Finally, we consider the limit behavior of the Stanley depth of symbolic powers of a squarefree monomial ideal. We also introduce a method for comparing the Stanley depth of factors of monomial ideals.</p> ER -