# Coordination sequences for root lattices and related graphs

@article{Baake1997CoordinationSF, title={Coordination sequences for root lattices and related graphs}, author={Michael Baake and Uwe Grimm}, journal={arXiv: Statistical Mechanics}, year={1997} }

The coordination sequence s(k) of a graph counts the number of its vertices which have distance k from a given vertex, where the distance between two vertices is defined as the minimal number of bonds in any path connecting them. For a large class of graphs, including in particular the classical root lattices, we present the coordination sequences and their generating functions, summarizing and extending recent results of Conway and Sloane. A possible application to the theory of critical…

## 33 Citations

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We consider averaged shelling and coordination numbers of aperiodic tilings. Shelling numbers count the vertices on radial shells around a vertex. Coordination numbers, in turn, count the vertices on…

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