Andreea I. Bordianu

activity

20212026

collaborators

7 papers

math.AC2026

On the Hilbert depth of a special class of squarefree monomial ideals

Andreea I. Bordianu, Mircea Cimpoeas

Let $r$ and $n$ be two positive integers and $S = K [x_{1}, \dots, x_{n + r - 1}]$ , the ring of polynomials in $n + r - 1$ variable, over a field $K$ . We consider the squarefree monomial ideal $…

math.AC2026

On the Hilbert depth of the quotient ring of the edge ideal of a complete bipartite graph

Andreea I. Bordianu, Mircea Cimpoeas

Let $n \geq m$ be two positive integers, $S_{n, m} = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{m}]$ and $I_{n, m} = (x_{i} y_{j} : 1 \leq i \leq n, 1 \leq j \leq m) \subset S_{n, m}$ the edge ideal of a complet…

math.AC2024

On the Stanley depth and Hilbert depth of some classes of edge ideals of graphs

Andreea I. Bordianu, Mircea Cimpoeas

We study the Stanley depth and the Hilbert depth of the edge ideals of path graphs, cycle graphs, generalized star graphs and double broom graphs.

math.AC2024

Comparing Hilbert depth of $I$ with Hilbert depth of $S / I$ . III

Andreea I. Bordianu, Mircea Cimpoeas

Let $I$ be a squarefree monomial ideal of $S = K [x_{1}, \dots, x_{n}]$ . We prove that if $hdepth (S / I) \leq 8$ or $n \leq 10$ then $\operatorname{hdepth}(I)\geq \operatorname{…

math.AC2024

Comparing Hilbert depth of $I$ with Hilbert depth of $S / I$ . II

Andreea I. Bordianu, Mircea Cimpoeas

Let $I$ be a squarefree monomial ideal of $S = K [x_{1}, \dots, x_{n}]$ . We prove that if $hdepth (S / I) \leq 6$ of $n \leq 9$ then $\operatorname{hdepth}(I)\geq \operatorname{h…

math.AC2024

Comparing Hilbert depth of $I$ with Hilbert depth of $S / I$

Andreea I. Bordianu, Mircea Cimpoeas

Let $I$ be a monomial ideal of $S = K [x_{1}, \dots, x_{n}]$ . We show that the following are equivalent: (i) $I$ is principal, (ii) $hdepth (I) = n$ , (iii) $\operatorname{hdept…

On the Hilbert depth of a special class of squarefree monomial ideals

On the Hilbert depth of the quotient ring of the edge ideal of a complete bipartite graph

On the Stanley depth and Hilbert depth of some classes of edge ideals of graphs

Comparing Hilbert depth of I with Hilbert depth of S/I. III

Comparing Hilbert depth of I with Hilbert depth of S/I. II

Comparing Hilbert depth of I with Hilbert depth of S/I

Comparing Hilbert depth of $I$ with Hilbert depth of $S / I$ . III

Comparing Hilbert depth of $I$ with Hilbert depth of $S / I$ . II

Comparing Hilbert depth of $I$ with Hilbert depth of $S / I$