Upper Bounds for the Connective Constant of Self-Avoiding Walks

  title={Upper Bounds for the Connective Constant of Self-Avoiding Walks},
  author={Sven Erick Alm},
  journal={Combinatorics, Probability & Computing},
We present a method for obtaining upper bounds for the connective constant of selfavoiding walks. The method works for a large class of lattices, including all that have been studied in connection with self-avoiding walks. The bound is obtained as the largest eigenvalue of a certain matrix. Numerical application of the method has given improved bounds for all lattices studied, e.g. ji < 2.696 for the square lattice, n < 4.278 for the triangular lattice and n < 4.756 for the simple cubic lattice… CONTINUE READING
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