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Simplicial Trees are Sequentially Cohen-Macaulay

Sara Faridi
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Abstract

This paper uses dualities between facet ideal theory and Stanley-Reisner theory to show that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay. The proof involves showing that the Alexander dual (or the cover dual, as we call it here) of a simplicial tree is a componentwise linear ideal. We conclude with additional combinatorial properties of simplicial trees.

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Sara Faridi. 2003-08-27. Simplicial Trees are Sequentially Cohen-Macaulay. https://arxiv.org/abs/math/0308264

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