Empty simplices of polytopes and graded Betti numbers

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dc.creatorNagel, Uwe
dc.date2005-12-14
dc.date.accessioned2026-07-07T06:55:12Z
dc.date.available2026-07-07T06:55:12Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/math/0512297
dc.identifierhttp://arxiv.org/abs/math/0512297
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106205
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.titleEmpty simplices of polytopes and graded Betti numbers
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