求解n = 6维格球覆盖问题的里程碑。

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-01-01 DOI:10.1107/S2053273324011513

Frank Vallentin

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引用次数: 0

摘要

在给定的维度上对（原始的、一般的）平行四面体进行完全分类是一项具有挑战性的计算任务。自最后一个维度n = 5的分类完成以来，已经过去了近50年。这种分类的一个应用是解决相应维数的格球覆盖问题。Dutour sikiriki & van Woerden的论文[晶体学报]。（2025）， A81, https://doi.org/10.1107/S2053273324010143]标志着维度n = 6的分类工作的一个里程碑。它提供了所有原始等边域的完整分类；在这里，原始平行四面体是基于它们的面向量来识别的。

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A milestone for the solution to the lattice sphere covering problem in dimension n = 6.

The complete classification of (primitive, generic) parallelohedra in a given dimension is a challenging computational task. Nearly 50 years have passed since the classification for the last dimension, n = 5, was completed. One application of such a classification is in solving the lattice sphere covering problem for the corresponding dimension. The paper by Dutour Sikirić & van Woerden [Acta Cryst. (2025), A81, https://doi.org/10.1107/S2053273324010143] marks a milestone in the classification effort for dimension n = 6. It provides a complete classification of all primitive iso-edge domains; here primitive parallelohedra are identified based on their facet vectors.

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.