Silviu Bălănescu

activity

20232025

most citedDepth and Stanley depth of powers of the path ideal of a path graph

1 citations · 1 across the 12 of their papers we have counts for

collaborators

14 papers

math.AC2025

On the Hilbert depth of the quotient ring of the edge ideal of a star graph

Silviu Balanescu, Mircea Cimpoeas, Mihai Cipu

Let $S_{n} = K [x_{1}, \dots, x_{n}, y]$ and $I_{n} = (x_{1} y, x_{2} y, \dots, x_{n} y) \subset S_{n}$ be the edge ideal of star graph. We prove that $\operatorname{hdepth}(S_n/I_n)\geq \left\lceil \frac{n}{2…

math.AC2024

Graded Betti numbers of powers of path ideals of paths

Silviu Balanescu, Mircea Cimpoeas, Thanh Vu

Let $I_{n, m} = (x_{1} \dots x_{m}, x_{2} \dots x_{m + 1}, \dots, x_{n + 1} x_{n + 2} \dots x_{n + m})$ be the $m$ -path ideal of a path of length $n + m - 1$ over a polynomial ring $S = \mathrm{k}[…

math.AC2024

Betti numbers of powers of path ideals of cycles

Silviu Balanescu, Mircea Cimpoeas, Thanh Vu

Let $J_{n, m} = (x_{1} \dots x_{m}, x_{2} \dots x_{m + 1}, \dots, x_{n} x_{1} \dots x_{m - 1})$ be the $m$ -path ideal of a cycle of length $n \geq 5$ over a polynomial ring $S = k[x_1,\ldots,x_n…

math.NT2024

On the Hilbert depth of quadratic and cubic functions

Mircea Cimpoeas, Silviu Balanescu

Given a numerical function $h : Z_{\geq 0} \to Z_{\geq 0}$ with $h (0) > 0$ , the Hilbert depth of $h$ is $\operatorname{hdepth}(h)=\max\{d\;:\;\sum\limits_{j=0}^k (-1)^{k-…

math.AC2024

Depth and Stanley depth of powers of the path ideal of a cycle graph. II

Silviu Balanescu, Mircea Cimpoeas

Let $J_{n, m} := (x_{1} x_{2} \dots x_{m}, x_{2} x_{3} \dots x_{m + 1}, \dots, x_{n - m + 1} \dots x_{n}, x_{n - m + 2} \dots x_{n} x_{1}, \dots, x_{n} x_{1} \dots x_{m - 1})$ be the $m$ -path ideal of the cycl…

math.AC2023

Remarks on the Hilbert depth of powers of the maximal graded ideal

Silviu Balanescu, Mircea Cimpoeas

Let $m = (x_{1}, \dots, x_{n})$ be the maximal graded ideal of $S := K [x_{1}, \dots, x_{n}]$ . We present a new method for computing the Hilbert depth of powers of $m$ .

math.AC2023

Remarks on the Hilbert depth of squarefree monomial ideals

Silviu Balanescu, Mircea Cimpoeas

Let $K$ be a infinite field, $S = K [x_{1}, \dots, x_{n}]$ and $0 \subset I ⊊ J \subset S$ two squarefree monomial ideals. In a previous paper we proved a new formula for the Hilbert…

math.NT2023

On the arithmetic Hilbert depth

Silviu Balanescu, Mircea Cimpoeas

Let $h : Z \to Z_{\geq 0}$ be a nonzero function with $h (k) = 0$ for $k ≪ 0$ . We define the Hilbert depth of $h$ by $\operatorname{hdepth}(h)=\max\{d\;:\; \sum_{j\leq…

math.AC2023

On the Hilbert depth of the Hilbert function of a finitely generated graded module

Silviu Balanescu, Mircea Cimpoeas

Let $K$ be a field, $A$ a standard graded $K$ -algebra and $M$ a finitely generated graded $A$ -module. Inspired by our previous works, we study the Hilbert depth of $h_{M}$ , that is $…

math.AC2023

Several combinatorial inequalities related to squarefree monomial ideals

Silviu Balanescu, Mircea Cimpoeas

Let $K$ be a field and $S = K [x_{1}, \dots, x_{n}]$ , the ring of polynomials in $n$ variables, over $K$ . Using the fact that the Hilbert depth is an upper bound for the Stanley depth of a…

math.AC2023

On the Hilbert depth of certain monomial ideals and applications

Silviu Balanescu, Mircea Cimpoeas

We study the Stanley depth and the Hilbert depth for $I$ and $S / I$ , where $I \subset S = K [x_{1}, \dots, x_{N}]$ is the intersection of monomial prime ideals with disjoint sets of variable…

math.AC2023

On the Hilbert depth of monomial ideals

Silviu Balanescu, Mircea Cimpoeas, Christian Krattenthaler

Let $S = K [x_{1}, \dots, x_{n}]$ be the ring of polynomials over a field $K$ . Given two monomial ideals $0 \subset I ⊊ J \subset S$ , we present a new method to compute the Hilbert…

math.AC2023★ 1 cited

Depth and Stanley depth of powers of the path ideal of a path graph

Silviu Balanescu, Mircea Cimpoeas

Let $I_{n, m} := (x_{1} x_{2} \dots x_{m}, x_{2} x_{3} \dots x_{m + 1}, \dots, x_{n - m + 1} \dots x_{n})$ be the $m$ -path ideal of the path graph of length $n$ , in the ring $S = K [x_{1}, \dots, x_{n}]$ .…

math.AC2023

Depth and Stanley depth of powers of the path ideal of a cycle graph

Silviu Balanescu, Mircea Cimpoeas