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Abstract: We use the notions of reflexivity and of reflexive dimensions in order tointroduce probability measures for lattice polytopes and initiate theinvestigation of their statistical properties. Examples of applications todiscrete geometry include a study of randomness of self-duality of reflexivepolytopes and implications for expectation values of the numbers of suchpolytopes in higher dimensions. We also discuss enumeration problems andrelated algorithms and point out interesting open problems. In this context wedefine the notion of IP-confined polytopes. Our new results include the list ofIP-simplices in 3 dimensions that are not IP-confined. The main motivation forthe study of these issues comes from applications in algebraic geometry andstring theory.

Autor: Maximilian Kreuzer

Fuente: https://arxiv.org/

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