2009/12/10 by Samuel Kolins, Kolins, Samuel
Mathematics · #13F55 #52B05 #57Q15 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:13F55 #msc:52B05 #msc:57Q15
paper · pdf · doi:10.48550/arxiv.0912.2091
24 pages
arxiv created 2009/12/10 · arxiv updated 2010/01/07
We describe two methods for showing that a vector can not be the f-vector of a homology d-ball. As a consequence, we disprove a conjectured characterization of the f-vectors of balls of dimension five and higher due to Billera and Lee. We also provide a construction of triangulated balls with various f-vectors. We show that this construction obtains all possible f-vectors of three and four dimensional balls and we conjecture that this result also extends to dimension five.