Counting lattice animals in high dimensions

  title={Counting lattice animals in high dimensions},
  author={Sebastian Luther and Stephan Mertens},
  journal={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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