相关论文: Edge ideals and their asymptotic syzygies

Let $G$ be a graph and $I=I(G)$ be its edge ideal. When $G$ is the clique sum of two different length odd cycles joined at single vertex then we give an explicit description of the symbolic powers of $I$ and compute the Waldschmidt…

Recently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior of several algebraic and homological invariants along such…

Let $R = \mathbb{K}[x_1, \ldots, x_n]$ and $I \subset R$ be a homogeneous ideal. In this article, we first obtain certain sufficient conditions for the subadditivity of $R/I$. As a consequence, we prove that if $I$ is generated by…

The aim of this work is to compare symbolic and ordinary powers of monomial ideals using commutative algebra and combinatorics. Monomial ideals whose symbolic and ordinary powers coincide are called Simis ideals. Weighted monomial ideals…

In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium…

Let $G$ be a graph with edge ideal $I(G)$. We recall the notions of $\min-match_{\{K_2, C_5\}}(G)$ and $\ind-match_{\{K_2, C_5\}}(G)$ from \cite{sy}. We show that $${\rm reg}(I(G)^s)\leq 2s+\min-match_{\{K_2, C_5\}}(G)-1,$$for all $s\geq…

In this paper we study the asymptotic behavior of the regularity of symbolic powers of ideals of points in a weighted projective plane. By a result of Cutkosky, Ein and Lazarsfeld, regularity of such powers behaves asymptotically like a…

In this paper,we introduce the monomial ideals I(H) associated to a special class of non uniform hypergraphs H(X; E; d) namely uniformly increasing hypergraphs. These ideals are named as inclusion ideals. In this paper, we discuss some…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

Let $D$ be a weighted oriented graph and $I(D)$ be its edge ideal. We provide one method to find all the minimal generators of $ I_{\subseteq C} $, where $ C $ is a maximal strong vertex cover of $D$ and $ I_{\subseteq C} $ is the…

This paper presents exact formulas for the regularity and depth of powers of edge ideals of an edge-weighted star graph. Additionally, we provide exact formulas for the regularity of powers of the edge ideal of an edge-weighted integrally…

Inspired by the notion of K\"onig graphs we introduce graded ideals of K\"onig type with respect to a monomial order $<$. It is shown that if $I$ is of K\"onig type, then the Cohen--Macaulay property of $\ini_<(I)$ does not depend on the…

Helical edge modes are characteristic of topological insulators in two dimensions. This paper demonstrates that helical edge modes remain across transitions to ordinary insulators or to semimetals under certain condition. Straight and…

Let $G$ be a simple graph on $n$ vertices and $\mathcal{I}_G$ denotes parity binomial edge ideal of $G$ in the polynomial ring $S = \mathbb{K}[x_1,\ldots, x_n, y_1, \ldots, y_n].$ We obtain a lower bound for the regularity of parity…

Let $K$ be a field, $S$ a polynomial ring and $E$ an exterior algebra over $K$, both in a finite set of variables. We study rigidity properties of the graded Betti numbers of graded ideals in $S$ and $E$ when passing to their generic…

Let $G$ be a graph with chordal complement and $I(G)$ its edge ideal. From work of Herzog, Hibi, and Zheng, it is known that $I(G)$ has linear quotients and all of its powers have linear resolutions. For edge ideals $I(G)$ arising from…

Let $R$ be a standard graded algebra over a field $k$ and $I$ be a homogeneous ideal of $R$. We study the question whether there is a constant $c$ such that $\Soc(H^{j}_{\fm}(R/I^t))_{<-ct}=0$ for all $t\geq 1$ and a variation of this…

We study (slope-)stability properties of syzygy bundles on a projective space P^N given by ideal generators of a homogeneous primary ideal. In particular we give a combinatorial criterion for a monomial ideal to have a semistable syzygy…

In this article, we introduce a relation including ideals of an evolution algebra and hereditary subsets of vertices of its associated graph and establish some properties among them. This relation allows us to determine maximal ideals and…

The main aim of the paper is to study in greater detail absolutely homogeneous structures (that is, objects with the property that each partial isomorphism extends to a global automorphism), with special emphasis on metric spaces and…