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

Oberwolfach'tan

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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Matematiksel konular

Cebir ve Sayılar Kuramı
Ayrık Matematik ve Matematiğin Temelleri
Geometri ve Topoloji

Yazar(lar)

Johannes Hofscheier, Alexander Kasprzyk

Lisans

DOI (Dijital nesne belirteci)

10.14760/SNAP-2025-008-EN

PDF indir

snapshot-2025-008.pdf

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Matematiksel konular

Cebir ve Sayılar Kuramı
Analiz
Eğitim ve Eğitim Bilimi
Ayrık Matematik ve Matematiğin Temelleri
Geometri ve Topoloji
Nümerik ve Hesap Analizi
Olasılık Kuramı ve İstatistik

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