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Upper Bounds for the Connective Constant of Self-Avoiding Walks

Published online by Cambridge University Press:  12 September 2008

Sven Erick Alm
Sven Erick Alm
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden
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Abstract

We present a method for obtaining upper bounds for the connective constant of self-avoiding 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. μ < 2.696 for the square lattice, μ < 4.278 for the triangular lattice and μ < 4.756 for the simple cubic lattice.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 2 , June 1993 , pp. 115 - 136
Copyright
Copyright © Cambridge University Press 1993

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