Coordination sequences of crystals are of quasi-polynomial type

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].

Source: Acta Crystallographica Section A - February 18, 2021 Category: Chemistry Authors: Nakamura, Y. Sakamoto, R. Mase, T. Nakagawa, J. Tags: coordination sequences graph theory Hilbert polynomial monoid theory research papers Source Type: research