# Counting lattice animals in high dimensions

@article{Luther2011CountingLA,
title={Counting lattice animals in high dimensions},
author={Sebastian Luther and Stephan Mertens},
journal={Journal of Statistical Mechanics: Theory and Experiment},
year={2011},
volume={2011},
pages={09026}
}
• Published 2011
• Mathematics, Physics
• Journal of Statistical Mechanics: Theory and Experiment
We present an implementation of Redelemeier's algorithm for the enumeration of lattice animals in high-dimensional lattices. The implementation is lean and fast enough to allow us to extend the existing tables of animal counts, perimeter polynomials and series expansion coefficients in d-dimensional hypercubic lattices for 3 ≤ d ≤ 10. From the data we compute formulae for perimeter polynomials for lattice animals of size n ≤ 11 in arbitrary dimension d. When amended by combinatorial arguments… Expand

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