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 H\`a
and Van Tuyl for computing the graded Betti numbers of simplicial trees.Comment: 17 pages, to appear; Connections Between Algebra and Geometry,
Birkhauser volume (2013