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

Let $\mathbf m=(x_1,\ldots,x_n)$ be the maximal graded ideal of $S:=K[x_1,\ldots,x_n]$. We present a new method for computing the Hilbert depth of $\mathbf m^t$, using the polarization and a combinatorial characterization of the Hilbert depth of a quotient of squarefree monomial ideals.

Authors

Mircea Cimpoeaş (ORCID: https://orcid.org/0000-0002-7774-9883)
Bălănescu Silviu (ORCID: https://orcid.org/0009-0008-3654-2254)

Institutions

University of Science and Technology (YE)
Universitatea Națională de Știință și Tehnologie Politehnica București (RO)

Publication Details

Journal: Annals of the University of Craiova Mathematics and Computer Science Series
Published: 2024-12-25
DOI: https://doi.org/10.52846/ami.v51i2.1911
Primary Topic: Commutative Algebra and Its Applications
Type: article
Field-Weighted Citation Impact: 0.00

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article

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

Mircea Cimpoeaş, Bălănescu Silviu

Dec 25, 2024

Annals of the University of Craiova Mathematics and Computer Science Series

Commutative Algebra and Its Applications

article

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

Mircea Cimpoeaş, Bălănescu Silviu

December 25, 2024article en

Abstract

Let $\mathbf m=(x_1,\ldots,x_n)$ be the maximal graded ideal of $S:=K[x_1,\ldots,x_n]$. We present a new method for computing the Hilbert depth of $\mathbf m^t$, using the polarization and a combinatorial characterization of the Hilbert depth of a quotient of squarefree monomial ideals.

Annals of the University of Craiova Mathematics and Computer Science SeriesVol. 51(2)

University of Science and Technology (YE), Universitatea Națională de Știință și Tehnologie Politehnica București (RO)

Openalex Percentile: Top 56%

Commutative Algebra and Its Applications

DOI Open Access PDF OpenAlex

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