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

Instantanés de recherche mathématique à 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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Sujet mathématique

Algèbre et théorie des nombres
Mathématiques discrètes et fondements des mathématiques
Géométrie et Topologie

Auteur(s)

Johannes Hofscheier, Alexander Kasprzyk

Licence

DOI

10.14760/SNAP-2025-008-EN

Télécharger PDF

snapshot-2025-008.pdf

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Sujet mathématique

Algèbre et théorie des nombres
Analyse
Pédagogie et éducation
Mathématiques discrètes et fondements des mathématiques
Géométrie et Topologie
Calcul numérique et calcul scientifique
Théorie des probabilités et statistique

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Chimie et sciences de la terre
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