标题： 准）晶体学的组合问题 显示英文标题

标题： Combinatorial problems of (quasi-)crystallography

摘要： 回顾了几种（准）晶体学中的组合问题，并特别强调了一种适用于晶体和准晶体的统一方法。 具体而言，我们研究了平面子晶格、相似子晶格、重合子晶格及其模量对应物，以及中心壳层和平均壳层。 相应的计数函数被封装在狄利克雷级数生成函数中，给出了三角晶格和十二次对称盾牌密铺的显式结果。 其他组合性质也作了简要总结。 显示英文摘要

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.