Integer decomposition property of polytopes
Sharon Robins
TL;DR
This paper investigates the integer decomposition property of certain lattice polytopes linked to smooth complete fans with limited rays, proving this property holds in these cases through classification and reduction techniques.
Contribution
It establishes the integer decomposition property for lattice polytopes associated with smooth complete fans with at most n+3 rays, expanding understanding in this area.
Findings
Proves the integer decomposition property for these polytopes.
Utilizes classification of smooth complete fans by Kleinschmidt and Batyrev.
Reduces higher-dimensional cases to lower-dimensional polytopes.
Abstract
We study the integer decomposition property of lattice polytopes associated with the -dimensional smooth complete fans with at most rays. Using the classification of smooth complete fans by Kleinschmidt and Batyrev and a reduction to lower dimensional polytopes, we prove the integer decomposition property for lattice polytopes in this setting.
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Taxonomy
TopicsPoint processes and geometric inequalities · Limits and Structures in Graph Theory · Computational Geometry and Mesh Generation