哈德维格猜想对强单型多面体成立

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-09-15 DOI:10.1007/s00013-025-02170-6

Vuong Bui

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引用次数: 0

摘要

组合几何中的哈德维格猜想指出，任何n维凸体最多可以被\(2^n\)个与原体同构的小体所覆盖。通过研究正规集的一个表征，证明了强单型多面体的Hadwiger猜想。（强）单型多面体的一个很好的性质是法线的集合决定了多面体的组合。

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Hadwiger’s conjecture holds for strongly monotypic polytopes

Hadwiger’s conjecture in combinatorial geometry states that any n-dimensional convex body can be covered by at most \(2^n\) smaller bodies homothetic to the original body. We prove Hadwiger’s conjecture for strongly monotypic polytopes by studying a characterization of the set of normals. One of the nice properties of (strongly) monotypic polytopes is that the set of normals decides the combinatorics of the polytope.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.