Is there a smooth lattice polytope which does not have the integer decomposition property?

Snapshots of modern mathematics from Oberwolfach

Is there a smooth lattice polytope which does not have the integer decomposition property?

We introduce Tadao Oda’s famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the two-dimensional case – including a proof of Pick’s Theorem, which elegantly relates the area of a lattice polygon to the number of lattice points it contains in its interior and on its boundary.

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Mathematical subjects

Algebra and Number Theory
Discrete Mathematics and Foundations
Geometry and Topology

Author(s)

Johannes Hofscheier, Alexander Kasprzyk

License

DOI (Digital Object Identifier)

10.14760/SNAP-2025-008-EN

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snapshot-2025-008.pdf

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snapshots: overview

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Mathematical subjects

Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

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