Abstract
Using a novel implementation of the Goulden–Jackson method, we compute new rigorous upper bounds for the connective constants of self-avoiding walks, breaking Alm's previous records for rectangular (hypercubic) lattices. We also give the explicit generating functions for memory ≤8. We then incorporate a numerical limit which gives bounds that are even better.
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Noonan, J. New Upper Bounds for the Connective Constants of Self-Avoiding Walks. Journal of Statistical Physics 91, 871–888 (1998). https://doi.org/10.1023/A:1023023831510
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DOI: https://doi.org/10.1023/A:1023023831510