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- Title
Empty Simplices of Polytopes and Graded Betti Numbers.
- Authors
Uwe Nagel
- Abstract
Abstract The conjecture of Kalai, Kleinschmidt, and Lee on the number of empty simplices of a simplicial polytope is established by relating it to the first graded Betti numbers of the polytope and applying a result of Migliore and the author. This approach allows us to derive explicit optimal bounds on the number of empty simplices of any given dimension. As a key result, we prove optimal bounds for the graded Betti numbers of any standard graded K-algebra in terms of its Hilbert function.
- Subjects
POLYTOPES; HYPERSPACE; TOPOLOGY; ALGEBRA
- Publication
Discrete & Computational Geometry, 2008, Vol 39, Issue 1-3, p389
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-008-9057-y