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}
}
  • N. Minh, N. Trung
  • Published 10 March 2010
  • Mathematics
  • arXiv: Commutative Algebra
View PDF on arXiv
49 Citations
Highly Influential Citations
6
Background Citations
16
Methods Citations
5
Results Citations
1

49 Citations

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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…
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References

SHOWING 1-10 OF 25 REFERENCES
Cohen-Macaulay quotients of polynomial rings
Symbolic powers of monomial ideals and vertex cover algebras
Cohen--Macaulaynees for symbolic power ideals of edge ideals
Combinatorial Characterizations of Generalized Cohen-macaulay Monomial Ideals
We give a generalization of Hochster's formula for local cohomolo-gies of square-free monomial ideals to monomial ideals, which are not necessarily square-free. Using this formula, we give…
Tetrahedral Curves
TLDR
It is shown that there is a large set of S-minimal curves such that each curve corresponds to a smooth point of a component of the Hilbert scheme and that this component has the expected dimension.
Symbolic Powers and Matroids
We prove that all the symbolic powers of a Stanley-Reisner ideal are Cohen-Macaulay if and only if the associated simplicial complex is a matroid.
Standard graded vertex cover algebras, cycles and leaves
The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining…
Combinatorics and commutative algebra
This text offers an overview of two of the main topics in the connections between commutative algebra and combinatorics. The first concerns the solutions of linear equations in non-negative integers.…
Matroid Representation of Clique Complexes
TLDR
The quality of a greedy algorithm for the maximum weighted clique problem from the viewpoint of matroid theory is approached and the necessary and sufficient number of matroids for the representation of all graphs with n vertices is determined.
Tetrahedral curves via graphs and Alexander duality
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