Simplicial Trees are Sequentially Cohen-Macaulay

Details Simplicial Trees are Sequentially Cohen-Macaulay Simplicial Trees are Sequentially Cohen-Macaulay

2003-08-27

arxiv.org/abs/math/0308264v1

Mathematics

Commutative Algebra

15 pages, 15 figures

Scientific paper

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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