Stanley depth and symbolic powers of monomial ideals - Seyed Fakhari, S. A. (Mathematica Scandinavica, 2017)
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≥ 1, the inequalities sdepth (S/I^(ks)) ≤ sdepth (S/I^(s)) and sdepth(I^(ks)) ≤ sdepth (I^(s)) hold. If moreover I is unmixed of height d, then we show that for every integer k≥1, sdepth(I^(k+d))≤ sdepth(I^(k) ) and sdepth(S/I^(k+d))≤ 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.