Classification of Formal Duality with an Example in Sphere Packing UROP + Final Paper
Classification of Formal Duality with an Example in Sphere Packing UROP + Final Paper
复制标题
形式对偶性的分类以及球堆积 UROP 最终论文中的示例
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Henry Cohn August
中科院分区：
文献类型：
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作者：
Jianqiao Xia;Henry Cohn August
我们研究了形式对偶的概念，这是由Cohn， Kumar， Reiher和sch<e:1> rmann通过研究欧几里得空间中粒子的基态构型而引入和发展的。本文证明了循环群和循环群的乘积中形式对偶对分类的一些结果。例如，在k≥2的形式为Z/2kZ的循环群中证明了原始形式对偶对的不存在性。结合sch<s:1>勒关于奇素数阶循环群的结果，完成了素数幂次循环群中形式对偶的分类。最后，我们利用正交关系考虑了Conway猜想的5维包中的形式对偶的存在性。
We study the notion of formal duality, which was introduced and developed by Cohn, Kumar, Reiher, and Schürmann through their study of ground state configurations of particles in Euclidean space. Here, we prove some results in the classification of formally dual pairs in cyclic groups and products of cyclic groups. For example, we prove the non-existence of primitive formally dual pairs in a cyclic group of the form Z/2kZ for k ≥ 2. Together with Schüler’s result on cyclic groups with odd prime order, this completes the classification of formally dual pairs in a cyclic group of prime power order. Finally, we use orthogonality relations to consider the existence of formally dual pairs in Conway’s conjectural 5 dimensional packings.