2008/09/06 by Maximilian Kreuzer, Kreuzer, Maximilian
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Topological and Geometric Data Analysis #hep-th #math.AG #math.CO
paper · pdf · doi:10.48550/arxiv.0809.1188
6 pages
arxiv created 2008/09/06 · openalex publication_date 2008/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use the notions of reflexivity and of reflexive dimensions in order to introduce probability measures for lattice polytopes and initiate the investigation of their statistical properties. Examples of applications to discrete geometry include a study of randomness of self-duality of reflexive polytopes and implications for expectation values of the numbers of such polytopes in higher dimensions. We also discuss enumeration problems and related algorithms and point out interesting open problems. In this context we define the notion of IP-confined polytopes. Our new results include the list of IP-simplices in 3 dimensions that are not IP-confined. The main motivation for the study of these issues comes from applications in algebraic geometry and string theory.