# Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

@article{Minh2010CohenMacaulaynessOM, title={Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals}, author={Nguy{\^e}n C{\^o}ng Minh and Ng{\^o} Vi{\^e}t Trung}, journal={arXiv: Commutative Algebra}, year={2010} }

## 49 Citations

Combinatorial characterizations of the Cohen-Macaulayness of the second power of edge ideals

- MathematicsJ. Comb. Theory, Ser. A
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Matroid configurations and symbolic powers of their ideals

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Star configurations are certain unions of linear subspaces of projective space that have been studied extensively. We develop a framework for studying a substantial generalization, which we call…

On the second powers of Stanley-Reisner ideals

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In this paper, we study several properties of the second power $I_{\Delta}^2$ of a Stanley-Reisner ideal $I_{\Delta}$ of any dimension. As the main result, we prove that $S/I_{\Delta}$ is Gorenstein…

Star configurations in $\mathbb P^n$

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Star configurations are certain unions of linear subspaces of projective space. They have appeared in several different contexts: the study of extremal Hilbert functions for fat point schemes in the…

Powers of Square-Free Monomial Ideals and Combinatorics

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- 2013

We survey research relating algebraic properties of powers of squarefree monomial ideals to combinatorial structures. In particular, we describe how to detect important properties of (hyper)graphs by…

Level property of ordinary and symbolic powers of Stanley-Reisner ideals

- MathematicsJournal of Algebra
- 2019

POWERS OF SQUAREFREE IDEALS AND COMBINATORICS

- Mathematics
- 2012

We survey research relating algebraic properties of powers of squarefree monomial ideals to combinatorial structures. In particular, we describe how to detect important properties of (hyper)graphs by…

$k$-clean monomial ideals

- Mathematics
- 2017

In this paper, we introduce the concept of $k$-clean monomial ideals as an extension of clean monomial ideals and present some homological and combinatorial properties of them. Using the hierarchal…

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