Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1807.07273

Hilbert Series Of Binomial Edge Ideals

Arvind Kumar·Rajib Sarkar
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let $G$ be a finite simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in the polynomial ring $S = K[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the Hilbert series of binomial edge ideal of decomposable graphs in terms of Hilbert series of its indecomposable subgraphs. Also, we compute the Hilbert series of binomial edge ideal of join of two graphs and as a consequence we obtain the Hilbert series of complete $k$-partite graph, fan graph, multi-fan graph and wheel graph.

Explore related subjects

math.AC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Arvind Kumar, Rajib Sarkar. 2019-03-24. Hilbert Series Of Binomial Edge Ideals. https://arxiv.org/abs/1807.07273

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Structure of irreducible homomorphisms to/from free and injective modules

Let $R$ be a commutative noetherian local ring. We extend the work of the author and Takahashi by investigating the structure of irreducible monomorphisms originating from free modules in the category of finitely generated $R$-modules. In the case where $R$ is complete, we further study the structure of irreducible monomorphisms and epimorphisms to and from injective modules in the category of artinian $R$-modules.

math.AC↗
arXiv2026

Systems of parameters consisting of linear forms for monomial ideal quotients

Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring over a field $K$ and let $I$ be a monomial ideal of $S$. We classify linear systems of parameters of $S/I$ over any field $K$ using linear algebra and show explicit linear systems of parameters when $K$ has at least $n$ elements. If $I(G)$ is the edge ideal of a perfect graph $G$, a cycle or the complement of a cycle, we show that $S/I(G)$ has a 0-1 linear system of parameters, and for graphs with independence number equal to $2$, we characterize when $S/I(G)$ has a 0-1 linear system of parameters.

math.AC↗
arXiv2026

Primality of dilated closed path polyominoes

In this paper we define a novel product on polyominoes called the tensor product of polyominoes. Using a special case of this product which we name a dilation, we construct a new class of polyominoes called the dilated closed paths. This class is a ''thick'' generalization of Cisto and Navarra's class of closed paths (arXiv:2006.13935). We prove the Zig-Zag Walk Conjecture for this new class thereby fully characterizing primality for its associated polyomino ideals.

math.AC↗