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The Skeleta of a Shellable Complex
by
Jay Schweig
University of Kansas
When K is a shellable complex, its first barycentric subdivision admits a natural coloring. We show that (almost) any color-selected subcomplex obtained in this fashion admits a convex-ear decomposition, proving several new h-vector inequalities for such complexes. Using this decomposition, we prove some interesting facts about the flag h-vector of a Cohen-Macaulay complex's face poset. Finally, we discuss some new conjectures suggested by our results.
Date received: February 19, 2009
Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayf-29.