Abstract

Combinatorial techniques are outlined through generalization Sheehan’s version of Pόlya’s theorem extended to all irreducible representations of the dihedral point group aimed at applications to nanotube enumerations. Furthermore we invoke the Euler Totem function for a cylindrical nanotube of any length and circumference. General expressions for the generalized character cycle indices are derived in order to enumerate chiral, achiral and stereo isomers of polysubstituted nanotube of any length and circumference. Remarkable connection with bondonic theory and its implications in potential tree enumeration is also originally initiated here. We have constructed the combinatorial enumeration tables for heterosubstituted nanotubes up to 100 vertices on the circular cross section and up to 100 tube length. The heterosubstituted nanotubes composed of carbon and nitrogen or tubes made of boron and nitrogen are of considerable interest due to their important optical properties, energy storage and in applications as high energy novel materials. Thus the developed techniques could have applications in the development of these materials and in the generation of combinatorial libraries of heteronanotubes.

摘要

通过推广 Sheehan 版本的 Pólya 定理来概述组合技术，该定理扩展到旨在应用于纳米管枚举的二面角点群的所有不可约表示。此外，我们为任意长度和周长的圆柱形纳米管调用欧拉图腾函数。为了列举任意长度和周长的多取代纳米管的手性、非手性和立体异构体，推导出广义特征循环指数的一般表达式。与bondonic 理论的显着联系及其在潜在树枚举中的含义也最初是从这里开始的。我们已经为圆形横截面上最多 100 个顶点和最多 100 个管长的异取代纳米管构建了组合枚举表。由碳和氮组成的异取代纳米管或由硼和氮制成的管由于其重要的光学性质、能量存储和作为高能新型材料的应用而受到相当大的关注。因此，所开发的技术可以在这些材料的开发和异质纳米管组合库的生成中得到应用。