f-Vectors of Triangulated Balls
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- Kolins, S. Discrete Comput Geom (2011) 46: 427. doi:10.1007/s00454-010-9300-1
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We describe two methods for showing that a vector cannot 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.