Discrete & Computational Geometry

, Volume 46, Issue 3, pp 427–446

f-Vectors of Triangulated Balls



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.


f-vectors Face ring Minimal free resolution 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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