Related papers: Sequentially Cohen-Macaulay mixed product ideals
We associate a {\it skew tableau ideal} to each filling of a skew Ferrers diagram with positive integers. We classify all unmixed and sequentially Cohen-Macaulay skew tableau ideals. Consequently, we classify all Cohen-Macaulay, Buchsbaum,…
Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all…
We compute some algebraic invariants (e.g. depth, Castelnuovo - Mumford regularity) for a special class of monomial ideals, namely the ideals of mixed products. As a consequence, we characterize the Cohen-Macaulay ideals of mixed products.
In this paper we provide a full combinatorial characterization of sequentially Cohen-Macaulay binomial edge ideals of closed graphs. In addition, we show that a binomial edge ideal of a closed graph is approximately Cohen-Macaulay if and…
All Cohen--Macaulay polymatroidal ideals are classified. The Cohen--Macaulay polymatroidal ideals are precisely the principal ideals, the Veronese ideals, and the squarefree Veronese ideals.
The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown…
We prove that wheels and block graphs have sequentially Cohen-Macaulay binomial edge ideals. Moreover, we provide a construction of new families of sequentially Cohen-Macaulay graphs by cones.
We compute the Betti numbers of the resolution of a special class of square-free monomial ideals, the ideals of mixed products. Moreover when these ideals are Cohen-Macaulay we calculate their type.
We classify all binomial edge ideals that are complete intersection and Cohen-Macaulay almost complete intersection. We also describe an algorithm and provide an implementation to compute primary decomposition of binomial edge ideals.
Cohen Macaulay property of fiber cones of ideals is characterized in terms of its Hilbert series. Hilbert series of fiber cones of ideals with minimal mixed multiplicity is calculated. It is proved that the fiber cone of an m-primary ideal…
We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen--Macaulay.
In this paper we discuss the problem of characterizing the Cohen-Macaulay property of certain families of monomial ideals with fixed radical. More precisely, we consider generically complete intersection monomial ideals whose radical…
We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen-Macaulay. As an application, we give a complete characterization of the…
This paper studies the question of when the Rees algebras associated to arbitrary filtration of ideals are sequentially Cohen-Macaulay. Although this problem has been already investigated by N. T. Cuong, S. Goto and H. L. Truong, their…
We classify the Cohen-Macaulay binomial edge ideals of cactus and bicyclic graphs.
Let $I$ be a monomial ideal of the polynomial ring $S=K[x_1,...,x_4]$ over a field $K$. Then $S/I$ is sequentially Cohen-Macaulay if and only if $S/I$ is pretty clean. In particular, if $S/I$ is sequentially Cohen-Macaulay then $I$ is a…
In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in \'etale algebras. We provide a bound for the type, and give formulas to compute it. We relate the type of the overorders of a given order to the size of…
In this paper, we introduce the multigraded modules of Borel type and extend several results from the theory of ideals of Borel type. We prove that modules of Borel type are sequentially Cohen Macaulay and pretty clean. Also, we give a…
We characterize the strongly Cohen-Macaulay ideals of second analytic deviation one in terms of depth properties of the powers of the ideal in the `standard range.' This provides an explanation of the behaviour of certain ideals that have…
The purpose of this paper is to present a family of Cohen-Macaulay monomial ideals such that their integral closures have embedded components and hence are not Cohen-Macaulay.