Empty simplices of polytopes and graded Betti numbers

Details Empty simplices of polytopes and graded Betti numbers Empty simplices of polytopes and graded Betti numbers

2005-12-14

arxiv.org/abs/math/0512297v1

Mathematics

Commutative Algebra

Scientific paper

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. The proof 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.

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