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arXiv · 1511.04676

On the Stanley-Reisner ideal of an expanded simplicial complex

Rahim Rahmati-Asghar·Somayeh Moradi
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Abstract

Let $Δ$ be a simplicial complex. We study the expansions of $Δ$ mainly to see how the algebraic and combinatorial properties of $Δ$ and its expansions are related to each other. It is shown that $Δ$ is Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum or $k$-decomposable, if and only if an arbitrary expansion of $Δ$ has the same property. Moreover, some homological invariants like the regularity and the projective dimension of the Stanley-Reisner ideals of $Δ$ and those of their expansions are compared.

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Rahim Rahmati-Asghar, Somayeh Moradi. 2016-01-13. On the Stanley-Reisner ideal of an expanded simplicial complex. https://arxiv.org/abs/1511.04676

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