A Note on Shelling

摘要

The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial and algebraic structure is well understood for crystals, but less so for non-periodic arrangements such as mathematical quasicrystals or model sets. In this note we summarise several aspects of central versus averaged shelling, illustrate the difference with explicit examples and discuss the obstacles that emerge with aperiodic order.