根据多宽度对宽度为 1 的晶格四面体进行分类

Pub Date : 2024-06-04 DOI:10.1007/s00454-024-00659-5

Girtrude Hamm

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引用次数: 0

摘要

我们引入了格子多面体的多宽，并以此对所有具有多宽（(1,w_2,w_3)）的格子四面体进行分类和计数。这种分类方法可以扩展为一种计算机算法，用来对任意给定多宽的网格四面体进行分类。我们用它来对小\(w_2\)和\(w_3\)的多宽\((2,w_2,w_3)\的格子四面体进行分类，并对任意多宽的格子四面体的计数函数提出猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Classification of Width 1 Lattice Tetrahedra by Their Multi-Width

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Classification of Width 1 Lattice Tetrahedra by Their Multi-Width

We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width \((1,w_2,w_3)\). The approach used in this classification can be extended into a computer algorithm to classify lattice tetrahedra of any given multi-width. We use this to classify tetrahedra with multi-width \((2,w_2,w_3)\) for small \(w_2\) and \(w_3\) and make conjectures about the function counting lattice tetrahedra of any multi-width.

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