On The Generalized Binomial Edge Ideals of Generalized Block Graphs
We compute the depth and (give bounds for) the regularity of generalized binomial edge ideals associated with generalized block graphs.
math.AC↗
arXiv subjects
Faryal Chaudhry
Publications and source records attributed to Faryal Chaudhry.
Ideals generated by $2$--minors of Hankel matrices
We study ideals generated by $2$--minors of generic Hankel matrices.
math.AC↗
Binomial edge ideals and rational normal scrolls
Let $X$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaulay. We find the minimal primes of $I_G$ and show that $I_G$ is a set theoretical complete intersection. Moreover, a sharp upper bound for the regularity of $I_G$ is given.
math.AC↗
On the binomial edge ideals of block graphs
We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity. Also, we show that the binomial edge ideal of a block graph has the same depth as its initial ideal.
math.AC↗