Silviu Bălănescu

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20232025

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

1 citations · 1 across the 4 of their papers we have counts for

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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.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…