171 research outputs found
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
Flows on Simplicial Complexes
Given a graph , the number of nowhere-zero \ZZ_q-flows is
known to be a polynomial in . We extend the definition of nowhere-zero
\ZZ_q-flows to simplicial complexes of dimension greater than one,
and prove the polynomiality of the corresponding function
for certain and certain subclasses of simplicial complexes.Comment: 10 pages, to appear in Discrete Mathematics and Theoretical Computer
Science (proceedings of FPSAC'12
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