Michael Baake, Uwe Grimm
A Note on Shelling
The paper is published: Discr. Comput. Geom. 30 (2003) 573-589

MSC:

52C20 Tilings in $2$ dimensions, See also {05B45, 51M20}

52C22 Tilings in $n$ dimensions, See also {05B45, 51M20}

05A15 Exact enumeration problems, generating functions, See Also

11R18 Cyclotomic extensions

11P21 Lattice points in specified regions

Abstract: 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.
Keywords: shelling functions, model sets, aperiodic order, cyclotomic fields