Fork-decompositions of matroids

For the abstract of this paper, please see the PDF file

g-elements, finite buildings and higher Cohen-Macaulay connectivity

The main result is a proof that the g-vector of a simplicial complex with a convex ear decomposition is an M-vector. This is a generalization of similar results for matroid complexes. We also show that a finite building has a convex ear decomposition. This leads to connections between higher Cohen-Macaulay connectivity and increasing h-vectors.Comment: To appear in JCT A. 20 page