‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...

Let R be a commutative ring with identity such that R admits at least two maximal ideals. In this article, we associate a graph with R whose vertex set is the set of all proper ideals I of R such that I is not contained in the Jacobson radical of R and distinct vertices I and J are joined by an edge if and only if I and J are not comparable under the inclusion relation. The aim of this article ...

In this article we associate to every lattice ideal IL,ρ ⊂ K[x1, . . . , xm] a cone σ and a graph Gσ with vertices the minimal generators of the Stanley-Reisner ideal of σ. To every polynomial F we assign a subgraph Gσ(F ) of the graph Gσ. Every expression of the radical of IL,ρ, as a radical of an ideal generated by some polynomials F1, . . . , Fs gives a spanning subgraph of Gσ, the ∪ s i=1Gσ...

In this article we consider the intersection graph G(R) of nontrivial proper ideals of a finite commutative principal ideal ring R with unity 1. Two distinct ideals are adjacent if they have non-trivial intersection. We characterize when the intersection graph is complete, bipartite, planar, Eulerian or Hamiltonian. We also find a formula to calculate the number of ideals in each ring and the d...

Masur and Smillie, 1993, proved precisely which singularity index lists arise from pseudo-Anosov mapping classes. In search of an analogous theorem for outer automorphisms of free groups, Handel and Mosher, 2011, ask: Is each connected, simplicial, (2r − 1)-vertex graph the ideal Whitehead graph of a fully irreducible φ ∈ Out(Fr)? We answer this question in the negative by exhibiting, for each ...