On the Stanley depth and the Schmitt-Vogel number of squarefree monomial ideals (Q1627500)

Let \(S=\mathbb{K}[x_1,\dots, x_n]\) be the polynomial ring in \(n\) variables over the field \(\mathbb{K}\). In the article under review, the author provides a lower bound for the Stanley depth of squarefree monomial ideals. In fact, for every monomial ideal \(I\), he introduces the notion of Schmitt-Vogel number, denoted by \(\mathrm{sv}(I)\) and prove that for every squarefree monomial ideal \(I\) , the inequalities \(\mathrm{sdepth}(I)\geq n-\mathrm{sv}(I)+1\) and \(\mathrm{sdepth}(S/I)\geq n-\mathrm{sv}(I)\) hold. For the entire collection see [Zbl 1400.13003].