Related papers: Decompositions of Cellular Binomial Ideals

In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Groebner basis of Z[x]-lattices, regular and coherent difference ascending…

The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible…

The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…

We construct an explicit equivariant cellular decomposition of the $(4n-1)$-sphere with respect to binary polyhedral groups, and describe the associated cellular homology chain complex. As a corollary of the binary octahedral case, we…

For an odd prime p the cohomology ring of an elementary abelian p-group is polynomial tensor exterior. We show that the ideal of essential classes is the Steenrod closure of the class generating the top exterior power. As a module over the…

In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for…

We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.

We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in…

We obtain an improved lower bound for the regularity of the binomial edge ideals of trees. We prove an upper bound for the regularity of the binomial edge ideals of certain subclass of block-graphs. As a consequence we obtain sharp upper…

We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…

We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…

This paper has two aims. The first is to study ideals of minors of matrices whose entries are among the variables of a polynomial ring. Specifically, we describe matrices whose ideals of minors of a given size are prime. The main result in…

We introduce a "workable" notion of degree for non-homogeneous polynomial ideals and formulate and prove ideal theoretic B\'ezout Inequalities for the sum of two ideals in terms of this notion of degree and the degree of generators. We…

Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholz-Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral…

Following the work of the first and last authors [2], we further analyze the structure of a zero set of a left ideal in the ring of central polynomials over the quaternion algebra H. We describe the "algebraic hull" of a point in H^n and…

In this article we describe cell decompositions of the moduli space of Riemann surfaces and their relationship to a Hurwitz problem. The cells possess natural linear structures and with respect to this they can be described as rational…

In the article "Non-commutative Grobner bases for commutative algebras", Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and initial ideals of those ideals in the free associative algebra which contain the…

Given an ample action of an inverse semigroup on a locally compact and Hausdorff topological space, we study the ideal structure of the crossed product algebra associated with it. By developing a theory of induced ideals, we manage to prove…

We discuss algebraic and homological properties of binomial edge ideals associated to graphs which are obtained by gluing of subgraphs and the formation of cones.

Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…