Computations of Colorings 7D‐Hypercube's Hyperplanes for All Irreducible Representations,Journal of Computational Chemistry

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Computations of Colorings 7D‐Hypercube's Hyperplanes for All Irreducible Representations
Journal of Computational Chemistry ( IF 3.4 ) Pub Date : 2019-12-22 , DOI: 10.1002/jcc.26118
Krishnan Balasubramanian ₁

Affiliation

In the present study, we compute and enumerate the colorings of 7D‐hypercube for all of its hyperplanes (q = 1–7) for all 110 irreducible representations (IRs) of the seventh‐dimensional hyperoctahedral group consisting of 645,120 symmetry operations. The computations of colorings of the 7D‐hypercube are motivated by a number of chemical and biological applications such as the 7D‐hypercube representation of the periodic table, hypercube representations of water heptamer clusters, genetic regulatory networks, isomerization graphs, massively large data representations, and so forth. We have employed the Möbius inversion technique combined with generalized character cycle indices for 110 IRs to compute the generating functions for colorings of seven different types of hyperplanes of the 7D‐hypercube varying from the vertices (q = 7) to hexeracts (q = 1) of the 7D‐hypercube. Explicit computed tables are provided for 110 IRs from q = 1 to q = 7 for the 7D‐hypercube. © 2019 Wiley Periodicals, Inc.

中文翻译：

所有不可约表示的着色 7D-Hypercube 超平面的计算

在本研究中，我们计算并枚举了由 645,120 个对称操作组成的七维超八面体群的所有 110 个不可约表示 (IR) 的 7D 超立方体的所有超平面 (q = 1-7) 的着色。7D 超立方体的着色计算受到许多化学和生物应用的启发，例如元素周期表的 7D 超立方体表示、水七聚体簇的超立方体表示、遗传调控网络、异构化图、大规模数据表示、等等。我们采用了莫比乌斯反演技术结合 110 个 IR 的广义字符循环索引来计算 7D 超立方体的七种不同类型的超平面着色的生成函数，这些超平面从顶点 (q = 7) 到六边形 (q = 1) 7D 超立方体。为 7D 超立方体提供了从 q = 1 到 q = 7 的 110 个 IR 的显式计算表。© 2019 威利期刊公司。

更新日期：2019-12-22

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