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

오버불파크에서 찍은 현대수학의 면모

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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수학적 주제

대수학/정수론

이산수학/수학기초론

기하학/위상수학

저자

Johannes Hofscheier, Alexander Kasprzyk

라이선스

CC BY-SA-4.0

디지털 객체 식별자(DOI)

10.14760/SNAP-2025-008-EN

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application/pdf

snapshot-2025-008.pdf

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수학적 주제

대수학/정수론

해석학

수학교육/교수법

이산수학/수학기초론

기하학/위상수학

수치해석/과학계산

확률론/통계학

다른 분야와의 연관성

화학 및 지구과학

컴퓨터 과학

공학

금융

인문/사회과학

생명 과학

물리학

수학 전반에 대한 소고

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