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

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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…