Add to ORKGBy a classical result of Brodmann, the function $\operatorname{depth} R/I^t$ is asymptotically a constant, i.e. there is a number $s$ such that $\operatorname{depth} R/I^t = \operatorname{depth} R/I^s$ for $t > s$. One calls the smallest number $s$ with this property the index of depth stability of $I$ and denotes it by $\operatorname{dstab}(I)$. This invariant remains mysterious til now. The main result of this paper gives an explicit formula for $\operatorname{dstab}(I)$ when $I$ is an arbitrary ideal generated by squarefree monomials of degree 2. That is the first general case where one can characterize $\operatorname{dstab}(I)$ explicitly. The formula expresses $\operatorname{dstab}(I)$ in terms of the associated graph. The proof involv...
In this dissertation, we study numerical invariants of minimal graded free resolu-tions of homogeneo...
Let $S=K[x_1,\ldots,x_n]$, where $K$ is a field, and $t_i(S/I)$ denotes the maximal shift in the min...
In this article, we establish initially regular sequences on cycles of the form $C_{3n+2}$ for $n\ge...
Let $I$ be a matroidal ideal of degrre $d$ of a polynomial ring $R=K[x_1,...,x_n]$, where $K$ is a f...
Let $I$ be the edge ideal of a cycle of length $n \ge 5$ over a polynomial ring $S = \mathrm{k}[x_1,...
The depth of squarefree powers of a squarefree monomial ideal is introduced. Let $I$ be a squarefree...
Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, th...
Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = \mat...
summary:Let $(R,\mathfrak m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We...
Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G)^2$ has a linear free resolut...
AbstractWe study the limit and initial behavior of the numerical function f(k)=depthS/Ik. General pr...
We study the algebraic invariants namely depth, Stanley depth, regularity and projective dimension o...
Let $G$ be a graph and $I(G)$ its edge ideal. In this paper, we completely determine the tuples $(\d...
on the occasion of their 70th birthdays Let I) J be two squarefree monomial ideals of a polynomial a...
In this dissertation, we study numerical invariants of minimal graded free resolutions of homogeneou...
In this dissertation, we study numerical invariants of minimal graded free resolu-tions of homogeneo...
Let $S=K[x_1,\ldots,x_n]$, where $K$ is a field, and $t_i(S/I)$ denotes the maximal shift in the min...
In this article, we establish initially regular sequences on cycles of the form $C_{3n+2}$ for $n\ge...
Let $I$ be a matroidal ideal of degrre $d$ of a polynomial ring $R=K[x_1,...,x_n]$, where $K$ is a f...
Let $I$ be the edge ideal of a cycle of length $n \ge 5$ over a polynomial ring $S = \mathrm{k}[x_1,...
The depth of squarefree powers of a squarefree monomial ideal is introduced. Let $I$ be a squarefree...
Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, th...
Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = \mat...
summary:Let $(R,\mathfrak m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We...
Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G)^2$ has a linear free resolut...
AbstractWe study the limit and initial behavior of the numerical function f(k)=depthS/Ik. General pr...
We study the algebraic invariants namely depth, Stanley depth, regularity and projective dimension o...
Let $G$ be a graph and $I(G)$ its edge ideal. In this paper, we completely determine the tuples $(\d...
on the occasion of their 70th birthdays Let I) J be two squarefree monomial ideals of a polynomial a...
In this dissertation, we study numerical invariants of minimal graded free resolutions of homogeneou...
In this dissertation, we study numerical invariants of minimal graded free resolu-tions of homogeneo...
Let $S=K[x_1,\ldots,x_n]$, where $K$ is a field, and $t_i(S/I)$ denotes the maximal shift in the min...
In this article, we establish initially regular sequences on cycles of the form $C_{3n+2}$ for $n\ge...