Mircea Cimpoeaş

works on

combinatorial algebra 1 depth of quotients 1 hilbert depth 1 polynomial rings 1 squarefree monomial ideals 1

From the 1 of 18 linked papers with an AI index.

activity

20242026

collaborators

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13 papers · 1 filter

math.AC2026

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

Andreea I. Bordianu, Mircea Cimpoeas

The paper studies the Hilbert depth of a family of squarefree monomial ideals defined in a polynomial ring, proving several results about the depth of the quotient ring and examini…

math.AC2026

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.AC2026

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.AC2026

On the Stanley length of monomial ideals

Mircea Cimpoeas

Let $S = K [x_{1}, \dots, x_{n}]$ be the ring of polynomials in $n$ variables over an arbitrary field $K$ . Given a finitely generated multigraded module $M$ , its Stanley length, denoted by…

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.AC2025

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…

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

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

On the Hilbert depth of certain monomial ideals and applications

On the Stanley length of monomial ideals

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

On the Hilbert depth of monomial ideals

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