(准)晶体学的组合问题
Combinatorial problems of (quasi-)crystallography
摘要:
综述了(准)晶体学的几个组合问题,特别强调了对晶体和准晶体都有效的统一方法。特别是,我们考虑平面子格,相似子格,重合子格,他们的模块对应,以及中央和平均壳。相应的计数函数被封装在Dirichlet级数生成函数中,并对三角形格子和十二重对称屏蔽平铺给出了明确的结果。其他组合性质进行了简要总结。
英文摘要:
Several combinatorial problems of (quasi-)crystallography are reviewed with special emphasis on a unified approach, valid for both crystals and quasicrystals. In particular, we consider planar sublattices, similarity sublattices, coincidence sublattices, their module counterparts, and central and averaged shelling. The corresponding counting functions are encapsulated in Dirichlet series generating functions, with explicit results for the triangular lattice and the twelvefold symmetric shield tiling. Other combinatorial properties are briefly summarised.
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