Related papers: Powers of componentwise linear ideals

We classify all unmixed monomial ideals I of codimension 2 which are generically a complete intersection and which have the property that the symbolic power algebra A(I) is standard graded. We give a lower bound for the highest degree of a…

Let $G$ be a $(C_4, 2K_2)$-free graph with edge ideal $I(G)\subset \Bbbk[x_1,\dots , x_n]$. We show that $I(G)^s$ has linear resolution for every $s\geq 2$. Also, we show that every power of the vertex cover ideal of $G$ has linear…

In a decision problem, observations are said to be material if they must be taken into account to perform optimally. Decision problems have an underlying (graphical) causal structure, which may sometimes be used to evaluate certain…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…

In this paper we study the normality of monomial ideals using linear programming and graph theory. We give normality criteria for monomial ideals, for ideals generated by monomials of degree two, and for edge ideals of graphs and clutters…

We prove formulas for the core of ideals that apply in arbitrary characteristic.

Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph…

This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers of a monomial ideal. We provide a full answer in the case of…

We classify all graphs $G$ satisfying the property that all matching powers $I(G)^{[k]}$ of the edge ideal $I(G)$ are bi-Cohen-Macaulay for $1\le k\le\nu(G)$, where $\nu(G)$ is the maximum size of a matching of $G$.

For the edge ideal I of an arbitrary simple graph G we describe the monomials of the saturation of a power of I in terms of (vertex) weighted graphs associated with the monomials. This description allows us to characterize the embedded…

The (proper) power graph of a group is a graph whose vertex set is the set of all (nontrivial) elements of the group and two distinct vertices are adjacent if one is a power of the other. Various kinds of planarity of (proper) power graphs…

In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several…

Let V be an infinite-dimensional vector space over a field of characteristic not equal to 2. We classify ideals of the Lie algebra gl(V) of all linear transformations of the space V.

We study powers of binomial edge ideals associated with closed and block graphs.

All powers of lexsegment ideals with linear resolution (equivalently, with linear quotients) have linear quotients with respect to suitable orders of the minimal monomial generators. For a large subclass of the lexsegment ideals the…

In this work, some combinatorial lower bound for regularity of powers of the edge ideal of a uniform hypergarph is gained. A family of hypergraphs whose regularity of edge ideal attains this bound and has a significant difference from the…

This paper investigates the symbolic powers of toric ideals. We first describe them in terms of the kernel of certain linear maps derived from the lattice structure of the toric ideal. Furthermore, we apply our results to show that symbolic…

In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.

In this note, we find a monomization of a certain power ideal associated to a directed graph. This power ideal has been studied in several settings. The combinatorial method described here extends earlier work of other, and will work on…