A good leaf order on simplicial trees
arXiv:1307.2190
Abstract
Using the existence of a good leaf in every simplicial tree, we order the facets of a simplicial tree in order to find combinatorial information about the Betti numbers of its facet ideal. Applications include an Eliahou-Kervaire splitting of the ideal, as well as a refinement of a recursive formula of Hà and Van Tuyl for computing the graded Betti numbers of simplicial trees.
17 pages, to appear; Connections Between Algebra and Geometry, Birkhauser volume (2013)