Coordination sequences for root lattices and related graphs
Statistical Mechanics
2008-02-03 v1 Combinatorics
Abstract
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 phenomena in lattice models is outlined.
Cite
@article{arxiv.cond-mat/9706122,
title = {Coordination sequences for root lattices and related graphs},
author = {Michael Baake and Uwe Grimm},
journal= {arXiv preprint arXiv:cond-mat/9706122},
year = {2008}
}
Comments
8 pages, LaTeX, 1 Postscript figure included, using epsf.sty and amssymb.sty