Coordination sequences of crystals are of quasi-polynomial type

Acta Crystallogr A Found Adv. 2021 Mar 1;77(Pt 2):138-148. doi: 10.1107/S2053273320016769. Epub 2021 Feb 18.


The coordination sequence of a graph measures how many vertices the graph has at each distance from a fixed vertex and is a generalization of the coordination number. Here it is proved that the coordination sequence of the graph obtained from a crystal is of quasi-polynomial type, as had been postulated by Grosse-Kunstleve et al. [Acta Cryst. (1996), A52, 879-889].

Keywords: Hilbert polynomial; coordination sequences; graph theory; monoid theory.