Mircea Cimpoeaş

activity

20062026

most citedStanley depth of complete intersection monomial ideals

35 citations · 204 across the 75 of their papers we have counts for

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Showing 2023Show all

9 papers · 1 filter

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…