Related papers: On the Stanley depth of a special class of Borel t…

We compute the Stanley depth for a particular, but important case, of the quotient of complete intersection monomial ideals. Also, in the general case, we give sharp bounds for the Stanley depth of a quotient of complete intersection…

We compute the Stanley depth of irreducible monomial ideals and we show that the Stanley depth of a monomial complete intersection ideal is the same as the Stanley depth of it's radical. Also, we give some bounds for the Stanley depth of a…

We give different bounds for the Stanley depth of a monomial ideal $I$ of a polynomial algebra $S$ over a field $K$. For example we show that the Stanley depth of $I$ is less or equal with the Stanley depth of any prime ideal associated to…

We compute the Stanley depth for the quotient ring of a square free Veronese ideal and we give some bounds for the Stanley depth of a square free Veronese ideal. In particular, it follows that both satisfy the Stanley's conjecture.

Let $S$ be a ring of polynomials in finitely many variables over a field. In this paper we give lower bounds for depth and Stanley depth of modules of the type $S/I^t$ for $t\geq1$, where $I$ is the edge ideal of some caterpillar and…

We give an upper bound for the Stanley depth of the edge ideal $I$ of a $k$-partite complete graph and show that Stanley's conjecture holds for $I$. Also we give an upper bound for the Stanley depth of the edge ideal of a $k$-uniform…

Let $\mathbb{K}$ be a field and $S=\mathbb{K}[x_1,...,x_n]$ be the polynomial ring in $n$ variables over the field $\mathbb{K}$. For every monomial ideal $I\subset S$, We provide a recursive formula to determine a lower bound for the…

In this paper we study depth and Stanley depth of the edge ideals and quotient rings of the edge ideals, associated to classes of graphs obtained by taking the strong product of two graphs. We consider the cases when either both graphs are…

We give an upper bound for the Stanley depth of the edge ideal of a complete $k$-partite hypergraph and as an application we give an upper bound for the Stanley depth of a monomial ideal in a polynomial ring $S$. We also give a lower and an…

We consider the face ideal associated to a line-type simplicial complex. We compute the \texttt{depth} and the \texttt{sdepth} for its quotient ring. In particular, the facet ideal and its quotient ring satisfy the Stanley inequality.

We prove that the edge ideals of line and cyclic graphs and their quotient rings satisfy the Stanley conjecture. We compute the Stanley depth for the quotient ring of the edge ideal associated to a cycle graph of length $n$, given a precise…

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by four squarefree monomials of degrees $d$ and others of…

Let $I$ be an intersection of three monomial prime ideals of a polynomial algebra $S$ over a field. We give a special Stanley decomposition of $I$ which provides a lower bound of the Stanley depth of $I$, greater than or equal to $\depth\…

Let $I\subset J$ be monomial ideals of a polynomial algebra $S$ over a field. Then the Stanley depth of $J/I$ is smaller or equal with the Stanley depth of $\sqrt{J}/\sqrt{I}$. We give also an upper bound for the Stanley depth of the…

We study the Stanley depth and the Hilbert depth of the edge ideals of path graphs, cycle graphs, generalized star graphs and double broom graphs.

We give tight bounds for the Stanley depth of the quotient ring of the path ideal of a cycle graph. In particular, we prove that it satisfies the Stanley inequality.

Let $J\subset I$ be monomial ideals. We show that the Stanley depth of $I/J$ can be computed in a finite number of steps. We also introduce the $\fdepth$ of a monomial ideal which is defined in terms of prime filtrations and show that it…

Let $I$ be a weakly polymatroidal ideal or a squarefree monomial ideal of a polynomial ring $S$. In this paper we provide a lower bound for the Stanley depth of $I$ and $S/I$. In particular we prove that if $I$ is a squarefree monomial…

Let $Q$ and $Q'$ be two monomial primary ideals of a polynomial algebra $S$ over a field. We give an upper bound for the Stanley depth of $S/(Q\cap Q')$ which is reached if $Q$,$Q'$ are irreducible. Also we show that Stanley's Conjecture…

Let $I$ be the edge ideal of a clutter $\mathcal{C}$ in a polynomial ring $S$. In this paper, we present estimations of the Stanley depth of $I$ as well as the Stanley regularity of $S/I$, in terms of combinatorial data from the clutter…