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- W4366999760 abstract "Given a simplicial complex $Delta$, we investigate how to construct a new simplicial complex $bar{Delta}$ such that the corresponding monomial ideals satisfy nice algebraic properties. We give a procedure to check the vertex decomposability of an arbitrary hypergraph. As a consequence, we prove that attaching non-pure skeletons at all vertices of a cycle cover of a simplicial complex $Delta$ results in a simplicial complex $bar{Delta}$ such that the associated hypergraph $mathcal{H}(bar{Delta})$ is vertex decomposable. Also, we prove that all symbolic powers of the cover ideal of $bar{Delta}$ are componentwise linear. Our work generalizes the earlier known result where non-pure complete graphs were added to all vertices of a cycle cover of a graph." @default.
- W4366999760 created "2023-04-27" @default.
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- W4366999760 date "2023-04-23" @default.
- W4366999760 modified "2023-10-01" @default.
- W4366999760 title "Vertex cover ideals of simplicial complexes" @default.
- W4366999760 doi "https://doi.org/10.48550/arxiv.2304.11640" @default.
- W4366999760 hasPublicationYear "2023" @default.
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