Simplicial Trees are Sequentially Cohen-Macaulay
arXiv:math/0308264
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.
15 pages, 15 figures