Discrete & Computational Geometry

, Volume 46, Issue 3, pp 427–446

f-Vectors of Triangulated Balls


DOI: 10.1007/s00454-010-9300-1

Cite this article as:
Kolins, S. Discrete Comput Geom (2011) 46: 427. doi:10.1007/s00454-010-9300-1


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-vectorsFace ringMinimal free resolution

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA